Question 1

An electric dipole is placed in a uniform electric field. Which statement about the potential energy of the dipole is correct?

Accepted Answer

Correct Option: A. Solution: The potential energy of a dipole in a uniform electric field is given by $U = -pE \cos 	heta$. It is maximum when $	heta = 90^\circ$, i.e., when the dipole is perpendicular to the field.

Question 2

A parallel plate capacitor is charged to a potential $V$ and then disconnected from the battery. If the separation between the plates is doubled, what happens to the energy stored in the capacitor?

Accepted Answer

Correct Option: D. Solution: The energy stored in a capacitor is given by $U = \frac{1}{2}CV^2$. When the separation is doubled, the capacitance halves, but since charge remains constant, the voltage doubles, leading to the energy becoming four times the initial value.

Question 3

A point charge $Q = 5 	imes 10^{-9} C$ is placed at the origin. Calculate the potential at a point $P$ located at $(3, 4, 0) \ m$ from the origin.

Accepted Answer

Correct Option: A. Solution: The potential $V$ due to a point charge is given by $$V = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r}$$, where $r$ is the distance from the charge. The distance $r$ is calculated using the Pythagorean theorem: $r = \sqrt{3^2 + 4^2} = 5 \ m$. Thus, $$V = \frac{9 	imes 10^9 	imes 5 	imes 10^{-9}}{5} = 900 \ V$$.

Question 4

If two capacitors with capacitances $C_1$ and $C_2$ are connected in series, what is the formula for the equivalent capacitance $C_{eq}$?

Accepted Answer

Correct Option: B. Solution: For capacitors in series, the equivalent capacitance $C_{eq}$ is given by $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2}$.

Question 5

A capacitor with capacitance $C$ is connected to a battery of voltage $V$. If the separation between the plates is doubled while keeping the charge constant, what happens to the energy stored in the capacitor?

Accepted Answer

Correct Option: C. Solution: The energy stored in a capacitor is given by $U = \frac{1}{2}CV^2$. If the plate separation is doubled, capacitance halves, but since $Q=CV$ is constant, $V$ doubles, leading to $U = \frac{1}{2}C(2V)^2 = 2U_0$.

Question 6

If the electric potential at a distance $r$ from a point charge $Q$ is $V$, what happens to the potential if the distance is doubled?

Accepted Answer

Correct Option: A. Solution: Electric potential due to a point charge is given by $V = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r}$. If the distance is doubled, the potential becomes $V' = \frac{1}{4\pi\varepsilon_0} \frac{Q}{2r} = \frac{V}{2}$.

Question 7

A dielectric slab is placed in a uniform external electric field $E_0$. Which of the following statements correctly describes the behavior of the electric field within the dielectric?

Accepted Answer

Correct Option: C. Solution: The external field induces a polarization in the dielectric, which creates an opposing field that reduces the overall electric field within the dielectric.

Question 8

What is the expression for the potential energy of a dipole in a uniform electric field?

Accepted Answer

Correct Option: B. Solution: The potential energy of a dipole in a uniform electric field is given by $U = -p \cdot E \cos 	heta$, where $p$ is the dipole moment, $E$ is the electric field, and $	heta$ is the angle between $p$ and $E$.

Question 9

A capacitor is filled with a dielectric material of susceptibility $\chi_e$. If the original capacitance was $C_0$, what is the new capacitance?

Accepted Answer

Correct Option: A. Solution: The capacitance of a capacitor filled with a dielectric is given by $C = C_0(1 + \chi_e)$, where $\chi_e$ is the electric susceptibility of the dielectric.

Question 10

Consider a system of three charges $q_1 = 2 	imes 10^{-6} C$, $q_2 = -3 	imes 10^{-6} C$, and $q_3 = 4 	imes 10^{-6} C$ placed at the vertices of an equilateral triangle with side length $0.1 \ m$. What is the potential energy of this system?

Accepted Answer

Correct Option: A. Solution: The potential energy of a system of three charges is given by $$U = \frac{1}{4\pi\varepsilon_0} \left( \frac{q_1q_2}{r_{12}} + \frac{q_2q_3}{r_{23}} + \frac{q_3q_1}{r_{31}} ight)$$. Substituting the given values, $$U = \frac{9 	imes 10^9}{0.1} \left( 2 	imes 10^{-6} 	imes -3 	imes 10^{-6} + -3 	imes 10^{-6} 	imes 4 	imes 10^{-6} + 4 	imes 10^{-6} 	imes 2 	imes 10^{-6} ight) = -0.27 \ J$$.

Question 11

Consider a point charge $Q$ placed at the origin. If a test charge $q$ is moved from a point at distance $r_1$ to a point at distance $r_2$ from the origin, what is the change in electric potential energy?

Accepted Answer

Correct Option: A. Solution: The change in electric potential energy is given by the difference in potential energy at the two points: $\Delta U = U_2 - U_1 = \frac{1}{4\pi\varepsilon_0} \left( \frac{Qq}{r_2} - \frac{Qq}{r_1} \right)$.

Question 12

A capacitor is charged to a potential difference $V$ and then disconnected from the battery. If a dielectric slab is inserted between the plates, what happens to the potential difference across the plates?

Accepted Answer

Correct Option: B. Solution: When a dielectric is inserted into a disconnected capacitor, the capacitance increases, and since $Q = CV$ and $Q$ is constant, $V$ must decrease.

Question 13

Consider a system of two charges $q_1$ and $q_2$ separated by a distance $r_{12}$. What is the potential energy of this system in the absence of any external field?

Accepted Answer

Correct Option: A. Solution: The potential energy of a system of two charges $q_1$ and $q_2$ separated by a distance $r_{12}$ is given by $U = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r_{12}}$. This expression arises from the work done in assembling the charge configuration.

Question 14

If the electric potential decreases uniformly from 10 V to 2 V over a distance of 4 meters, what is the magnitude of the electric field?

Accepted Answer

Correct Option: B. Solution: The electric field $E$ is given by $E = -\frac{dV}{dl}$. Here, $dV = 2 - 10 = -8$ V and $dl = 4$ m, so $E = -\frac{-8}{4} = 2$ V/m.

Question 15

Consider a parallel plate capacitor with a dielectric material inserted between the plates. If the dielectric constant is $\kappa$ and the initial capacitance without the dielectric is $C_0$, what is the new capacitance $C$ of the capacitor?

Accepted Answer

Correct Option: B. Solution: The capacitance of a capacitor with a dielectric is given by $C = \kappa C_0$, where $\kappa$ is the dielectric constant.

Question 16

Which of the following statements about equipotential surfaces is true?

Accepted Answer

Correct Option: B. Solution: Equipotential surfaces are perpendicular to electric field lines because no work is done in moving a charge along an equipotential surface.

Question 17

Consider a uniformly charged spherical shell with total charge $Q$ and radius $R$. What is the electric potential at a point inside the shell at a distance $r < R$ from the center?

Accepted Answer

Correct Option: A. Solution: Inside a uniformly charged spherical shell, the electric field is zero, and thus the potential is constant and equal to the potential at the surface. Therefore, the potential at any point inside is $\frac{Q}{4\pi\varepsilon_0 R}$.

Question 18

In a parallel plate capacitor, if the area of the plates is increased while keeping the separation constant, how does the electric field between the plates change?

Accepted Answer

Correct Option: C. Solution: The electric field $E$ between the plates of a capacitor is independent of the area and is given by $E = \frac{V}{d}$, where $V$ is the voltage across the plates and $d$ is the separation. Thus, increasing the area does not change the electric field.

Question 19

In the context of electrostatic potential, which statement is true regarding the potential difference between two points in an electric field?

Accepted Answer

Correct Option: B. Solution: The potential difference between two points in an electric field is path-independent, which is a characteristic of conservative fields.

Question 20

Which of the following statements correctly describes the relationship between electric field lines and equipotential surfaces?

Accepted Answer

Correct Option: B. Solution: Electric field lines are always perpendicular to equipotential surfaces. This is because if there were any component of the electric field along the surface, work would be done in moving a charge along the surface, contradicting the definition of an equipotential surface.

Question 21

Consider a parallel plate capacitor with plate area $A$ and separation $d$, filled with a dielectric of dielectric constant $\kappa$. If the dielectric is removed while the capacitor is connected to a battery, what happens to the capacitance and the charge on the capacitor?

Accepted Answer

Correct Option: A. Solution: The capacitance with the dielectric is $C = \kappa \varepsilon_0 \frac{A}{d}$. Removing the dielectric reduces the capacitance to $C' = \varepsilon_0 \frac{A}{d}$. Since the capacitor is connected to a battery, the voltage remains constant, so the charge $Q = CV$ remains the same.

Question 22

In a parallel plate capacitor, if the area of the plates is doubled and the distance between them is halved, how does the capacitance change?

Accepted Answer

Correct Option: C. Solution: The capacitance $C$ is proportional to the area $A$ and inversely proportional to the distance $d$ between the plates. Doubling $A$ and halving $d$ results in a capacitance that is four times the original value.

Question 23

Consider a charge $q$ placed in an external electric field with potential $V(r)$. If the potential energy $U$ of the charge is given by $U = qV(r)$, what happens to the potential energy if the charge is doubled and the potential remains the same?

Accepted Answer

Correct Option: A. Solution: The potential energy $U = qV(r)$ is directly proportional to the charge $q$. Therefore, if the charge is doubled, the potential energy also doubles.

Question 24

A charge is moved from point A to point B along an equipotential surface. What is the work done by the electric field?

Accepted Answer

Correct Option: C. Solution: Zero work is done when a charge is moved along an equipotential surface because the potential difference is zero.

Question 25

What is the expression for the electric potential $V$ due to a point charge $Q$ at a distance $r$ from the charge?

Accepted Answer

Correct Option: A. Solution: The electric potential $V$ due to a point charge $Q$ at a distance $r$ is given by $V = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r}$, where $\varepsilon_0$ is the permittivity of free space.

Question 26

Consider a dielectric slab placed in a uniform electric field. If the dielectric constant is $K$, how does the presence of the dielectric affect the electric field inside the slab?

Accepted Answer

Correct Option: C. Solution: The dielectric reduces the electric field inside it by a factor of $K$, the dielectric constant, due to the polarization of the dielectric material.

Question 27

What is the potential inside a uniformly charged spherical shell?

Accepted Answer

Correct Option: B. Solution: Inside a uniformly charged spherical shell, the electric field is zero, and the potential is constant and equal to the surface potential.

Question 28

Consider a system where a test charge $q$ is moved from point $R$ to point $P$ in an electrostatic field created by a charge $Q$. If the work done by the external force is $W_{RP}$, which of the following statements is true about the potential energy difference between points $R$ and $P$?

Accepted Answer

Correct Option: A. Solution: The potential energy difference between two points in an electrostatic field is equal to the work done by the external force in moving the charge from one point to another.

Question 29

A parallel plate capacitor with a dielectric constant $K$ is charged to a potential $V$. If the dielectric is removed while the capacitor remains connected to the battery, what happens to the charge on the capacitor?

Accepted Answer

Correct Option: C. Solution: When the dielectric is removed while the capacitor is connected to the battery, the potential difference remains constant (equal to the battery voltage), and hence the charge on the capacitor remains the same.

Question 30

For an electric dipole, the potential at a point on the equatorial plane is:

Accepted Answer

Correct Option: C. Solution: The potential due to an electric dipole on the equatorial plane is zero because the contributions from the positive and negative charges cancel each other out.

Question 31

What is the electric field just outside the surface of a charged conductor?

Accepted Answer

Correct Option: A. Solution: The electric field just outside the surface of a charged conductor is given by $E = \frac{\sigma}{\varepsilon_0} \hat{n}$, where $\sigma$ is the surface charge density and $\hat{n}$ is the unit vector normal to the surface.

Question 32

In a series capacitor circuit, if the charge on each capacitor is $Q$ and the potential differences across the capacitors are $V_1$, $V_2$, and $V_3$, which of the following statements is correct?

Accepted Answer

Correct Option: B. Solution: In a series circuit, the charge on each capacitor is the same, but the total potential difference is the sum of the potential differences across each capacitor: $V = V_1 + V_2 + V_3$.

Question 33

Which of the following statements is true regarding the relationship between the dielectric constant $K$, permittivity $\varepsilon$, and electric susceptibility $\chi_e$?

Accepted Answer

Correct Option: A. Solution: The dielectric constant $K$ is defined as $K = \varepsilon / \varepsilon_0$, and the electric susceptibility $\chi_e$ is related to the dielectric constant by $\chi_e = K - 1$.

Question 34

A proton is accelerated from rest through a potential difference of 1 million volts (1 MV). What is the kinetic energy gained by the proton in electron volts (eV)?

Accepted Answer

Correct Option: C. Solution: The kinetic energy gained by a charge when accelerated through a potential difference $V$ is given by $qV$. For a proton, $q = e = 1.6 	imes 10^{-19} 	ext{C}$. When accelerated through 1 MV, the energy gained is $1 	ext{ MeV}$, since $1 	ext{ MV} = 10^6 	ext{ V}$ and $1 	ext{ eV} = 1.6 	imes 10^{-19} 	ext{ J}$.

Question 35

In a capacitor system, if the charge on the capacitor is doubled, what happens to the electric field between the conductors?

Accepted Answer

Correct Option: C. Solution: The electric field in the region between the conductors is proportional to the charge $Q$. Therefore, if the charge is doubled, the electric field will also be doubled.

Question 36

What is the potential energy of a system of two charges $q_1$ and $q_2$ separated by a distance $r_{12}$?

Accepted Answer

Correct Option: A. Solution: The potential energy of a system of two charges is given by $U = \frac{1}{4\pi\varepsilon_0} \frac{q_1q_2}{r_{12}}$, which is directly proportional to the product of the charges and inversely proportional to the distance between them.

Question 37

Consider a charged conductor with a cavity. What is the electric field inside the cavity?

Accepted Answer

Correct Option: A. Solution: The electric field inside a cavity of a conductor is zero, regardless of the charge on the conductor or external fields. This is a result of electrostatic shielding.

Question 38

A uniformly charged spherical shell with charge $Q$ and radius $R$ is placed in an external electric field. What is the potential difference between the center of the shell and a point just outside the shell?

Accepted Answer

Correct Option: D. Solution: The potential inside the shell is constant and equal to the potential at the surface. The potential difference between the center and just outside the shell is due to the external field, which is $E \cdot R$, where $E$ is the external electric field.

Question 39

A spherical conductor is charged and placed in an external electric field. What is the electric field inside the conductor and at its surface?

Accepted Answer

Correct Option: A. Solution: The electric field inside a conductor is zero because charges redistribute to cancel any internal field. At the surface, the field is normal and proportional to the surface charge density $\sigma$.

Question 40

Consider a point charge $Q$ at the origin. Which of the following describes the nature of equipotential surfaces around this charge?

Accepted Answer

Correct Option: A. Solution: For a point charge, the equipotential surfaces are concentric spherical surfaces centered at the charge. This is because the potential $V$ at a distance $r$ from the charge is constant for a constant $r$, forming a sphere.

Question 41

In a uniform electric field $\vec{E}$, a dipole with dipole moment $\vec{p}$ is in stable equilibrium. Which of the following statements is true regarding the potential energy of the dipole?

Accepted Answer

Correct Option: C. Solution: The potential energy of a dipole in a uniform electric field is given by $U = -pE \cos 	heta$. In stable equilibrium, the dipole is aligned with the field ($	heta = 0^\circ$), making $\cos 	heta = 1$. Thus, $U = -pE$, which is the minimum potential energy.

Question 42

In a conductor, which of the following statements is true regarding the distribution of electric field and charge?

Accepted Answer

Correct Option: A. Solution: Inside a conductor, the electrostatic field is zero, and any excess charge resides on the surface due to the movement of free electrons until equilibrium is reached.

Question 43

Consider two closely spaced equipotential surfaces with potentials $V$ and $V + \delta V$. If a unit positive charge is moved from the surface with potential $V + \delta V$ to the surface with potential $V$, what is the relationship between the electric field $E$ and the potential difference?

Accepted Answer

Correct Option: B. Solution: The electric field $E$ is related to the potential difference by $E = -\frac{\delta V}{\delta l}$, where $\delta l$ is the perpendicular distance between the surfaces.

Question 44

Which of the following best describes electrostatic shielding?

Accepted Answer

Correct Option: A. Solution: Electrostatic shielding is the phenomenon where the electric field inside a conductor is zero, regardless of any external electric fields. This is due to the redistribution of charges on the conductor's surface.

Question 45

What is the work done by an external force in bringing a test charge $q$ from infinity to a point $P$ in an electric field?

Accepted Answer

Correct Option: A. Solution: The work done by an external force in bringing a test charge $q$ from infinity to a point $P$ is stored as potential energy at point $P$.

Question 46

Consider a charged conductor. Just outside the surface of the conductor, the electric field is given by $E = \frac{\sigma}{\varepsilon_0} \hat{n}$. Which of the following statements is true regarding the electric field inside and just outside the conductor?

Accepted Answer

Correct Option: A. Solution: Inside a conductor, the electric field is zero due to the redistribution of free charges. Just outside the surface, the electric field is normal to the surface due to the surface charge density $\sigma$.

Question 47

In a series combination of capacitors, which of the following statements is true?

Accepted Answer

Correct Option: B. Solution: In a series combination, the total potential difference is the sum of the individual potential differences across each capacitor.

Question 48

What is the equivalent capacitance of capacitors connected in parallel?

Accepted Answer

Correct Option: A. Solution: In a parallel combination, the equivalent capacitance is the sum of the individual capacitances: $C = C_1 + C_2 + C_3 + \ldots$.

Question 49

A dipole with moment $p$ is placed in a uniform electric field $E$. If the dipole is initially aligned at an angle $	heta_0$ to the field and is rotated to an angle $	heta_1$, what is the work done by the external torque?

Accepted Answer

Correct Option: A. Solution: The work done by the external torque is given by $W = pE(\cos	heta_0 - \cos	heta_1)$, which accounts for the change in potential energy as the dipole rotates in the field.

Question 50

In which orientation does a dipole achieve stable equilibrium in a uniform electric field?

Accepted Answer

Correct Option: C. Solution: A dipole achieves stable equilibrium when its dipole moment $p$ is parallel to the electric field $E$. In this orientation, the potential energy is minimized.

Question 51

How does a dielectric material behave when placed in an external electric field?

Accepted Answer

Correct Option: B. Solution: A dielectric polarizes in an external electric field, creating an induced dipole moment that reduces the net electric field inside the material.

Question 52

What is the role of polarization in a dielectric material when placed in an external electric field?

Accepted Answer

Correct Option: C. Solution: Polarization in a dielectric results in the formation of bound surface charges which create an internal field opposing the external field, thus reducing the net field inside.

Question 53

Consider an electric dipole placed at the origin. Which of the following expressions correctly represents the potential at a point located at a large distance from the dipole along the axial line?

Accepted Answer

Correct Option: A. Solution: The potential due to an electric dipole at a large distance along the axial line is given by $$V = \frac{1}{4\pi\varepsilon_0} \frac{p \cos 	heta}{r^2}$$, where $p$ is the dipole moment, $r$ is the distance from the dipole, and $	heta$ is the angle between the dipole axis and the position vector.

Question 54

In a dielectric material placed in an external electric field $E_0$, the induced surface charge density is $\sigma_p$. Which of the following correctly describes the effect of the dielectric on the external field?

Accepted Answer

Correct Option: C. Solution: The dielectric reduces the external field inside it due to the induced surface charges that partially oppose the external field.

Question 55

If three capacitors with capacitances $C_1 = 2 \mu F$, $C_2 = 3 \mu F$, and $C_3 = 5 \mu F$ are connected in parallel, what is the total capacitance?

Accepted Answer

Correct Option: A. Solution: For capacitors in parallel, the total capacitance is the sum of the individual capacitances: $C = C_1 + C_2 + C_3 = 2 \mu F + 3 \mu F + 5 \mu F = 10 \mu F$.

Question 56

What is the relationship between the dielectric constant $K$, permittivity $\varepsilon$, and the permittivity of free space $\varepsilon_0$?

Accepted Answer

Correct Option: A. Solution: The dielectric constant $K$ is defined as the ratio of the permittivity of the dielectric $\varepsilon$ to the permittivity of free space $\varepsilon_0$, i.e., $K = \varepsilon / \varepsilon_0$.

Question 57

A student mistakenly believes that in a series capacitor circuit, the equivalent capacitance is greater than the largest individual capacitance. Which concept would correct this misconception?

Accepted Answer

Correct Option: A. Solution: The correct concept is that the equivalent capacitance in a series circuit is always less than the smallest individual capacitance. This is because the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances.

Question 58

What is the energy gained by an electron when it is accelerated through a potential difference of 1 volt?

Accepted Answer

Correct Option: A. Solution: The energy gained by an electron accelerated through a potential difference of 1 volt is 1 electron volt (eV), which is equivalent to $1.6 	imes 10^{-19} 	ext{ J}$.

Question 59

When a dielectric material is placed in an external electric field, how does it affect the field inside the material?

Accepted Answer

Correct Option: D. Solution: In a dielectric, the external field induces dipole moments that create a field opposing the external field, reducing but not completely canceling it.

Question 60

Consider a parallel plate capacitor with plates of area $A$ and separation $d$. If the capacitor is filled with a dielectric material with dielectric constant $K$, what is the new capacitance of the capacitor?

Accepted Answer

Correct Option: B. Solution: The capacitance of a parallel plate capacitor filled with a dielectric is given by $C = \frac{K \varepsilon_0 A}{d}$, where $K$ is the dielectric constant.

Question 61

A charge-free cavity is present inside a conductor. If an external electric field is applied, what will be the electric field inside the cavity?

Accepted Answer

Correct Option: B. Solution: Inside a conductor with a charge-free cavity, the electric field is zero regardless of the external electric field. This is due to electrostatic shielding, where the conductor redistributes its charges to cancel the external field inside the cavity.

Question 62

What is the relation between the electric field $E$ and the electric potential $V$ in a region of space?

Accepted Answer

Correct Option: A. Solution: The electric field $E$ is related to the potential gradient as $E = -\frac{dV}{dl}$, indicating that the field points in the direction of steepest decrease of potential.

Question 63

If a conductor is placed in an external electric field, what happens to the field inside the conductor?

Accepted Answer

Correct Option: B. Solution: When a conductor is placed in an external electric field, free charges within the conductor move to cancel the field inside, resulting in a zero electric field inside the conductor.

Question 64

A capacitor is charged such that it stores an energy of $U = \frac{1}{2}CV^2$. If the voltage across the capacitor is doubled, what happens to the stored energy?

Accepted Answer

Correct Option: C. Solution: The energy stored in a capacitor is given by $U = \frac{1}{2}CV^2$. If the voltage is doubled, $V' = 2V$, then $U' = \frac{1}{2}C(2V)^2 = 2^2 	imes \frac{1}{2}CV^2 = 4U$. Therefore, the energy quadruples.

Electrostatic Potential a..

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Electrostatic Potential and Capacitance

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Multiple Choice Questions

Q1.An electric dipole is placed in a uniform electric field. Which statement about the potential energy of the dipole is correct?

Correct Answer: A

Q2.A parallel plate capacitor is charged to a potential VVV and then disconnected from the battery. If the separation between the plates is doubled, what happens to the energy stored in the capacitor?

Correct Answer: D

Q3.A point charge Q=5×10−9CQ = 5 \times 10^{-9} CQ=5×10−9C is placed at the origin. Calculate the potential at a point PPP located at (3,4,0) m(3, 4, 0) \ m(3,4,0) m from the origin.

Correct Answer: A

Q4.If two capacitors with capacitances C1C_1C1​ and C2C_2C2​ are connected in series, what is the formula for the equivalent capacitance CeqC_{eq}Ceq​?

Correct Answer: B

Q5.A capacitor with capacitance CCC is connected to a battery of voltage VVV. If the separation between the plates is doubled while keeping the charge constant, what happens to the energy stored in the capacitor?

Correct Answer: C

Q6.If the electric potential at a distance rrr from a point charge QQQ is VVV, what happens to the potential if the distance is doubled?

Correct Answer: A

Q7.A dielectric slab is placed in a uniform external electric field E0E_0E0​. Which of the following statements correctly describes the behavior of the electric field within the dielectric?

Correct Answer: C

Q8.What is the expression for the potential energy of a dipole in a uniform electric field?

Correct Answer: B

Q9.A capacitor is filled with a dielectric material of susceptibility χe\chi_eχe​. If the original capacitance was C0C_0C0​, what is the new capacitance?

Correct Answer: A

Correct Answer: A

Q11.Consider a point charge QQQ placed at the origin. If a test charge qqq is moved from a point at distance r1r_1r1​ to a point at distance r2r_2r2​ from the origin, what is the change in electric potential energy?

Correct Answer: A

Q12.A capacitor is charged to a potential difference VVV and then disconnected from the battery. If a dielectric slab is inserted between the plates, what happens to the potential difference across the plates?

Correct Answer: B

Q13.Consider a system of two charges q1q_1q1​ and q2q_2q2​ separated by a distance r12r_{12}r12​. What is the potential energy of this system in the absence of any external field?

Correct Answer: A

Q14.If the electric potential decreases uniformly from 10 V to 2 V over a distance of 4 meters, what is the magnitude of the electric field?

Correct Answer: B

Q15.Consider a parallel plate capacitor with a dielectric material inserted between the plates. If the dielectric constant is κ\kappaκ and the initial capacitance without the dielectric is C0C_0C0​, what is the new capacitance CCC of the capacitor?

Correct Answer: B

Q16.Which of the following statements about equipotential surfaces is true?

Correct Answer: B

Q17.Consider a uniformly charged spherical shell with total charge QQQ and radius RRR. What is the electric potential at a point inside the shell at a distance r<Rr < Rr<R from the center?

Correct Answer: A

Q18.In a parallel plate capacitor, if the area of the plates is increased while keeping the separation constant, how does the electric field between the plates change?

Correct Answer: C

Q19.In the context of electrostatic potential, which statement is true regarding the potential difference between two points in an electric field?

Correct Answer: B

Q20.Which of the following statements correctly describes the relationship between electric field lines and equipotential surfaces?

Correct Answer: B

Q21.Consider a parallel plate capacitor with plate area AAA and separation ddd, filled with a dielectric of dielectric constant κ\kappaκ. If the dielectric is removed while the capacitor is connected to a battery, what happens to the capacitance and the charge on the capacitor?

Correct Answer: A

Q22.In a parallel plate capacitor, if the area of the plates is doubled and the distance between them is halved, how does the capacitance change?

Correct Answer: C

Q23.Consider a charge qqq placed in an external electric field with potential V(r)V(r)V(r). If the potential energy UUU of the charge is given by U=qV(r)U = qV(r)U=qV(r), what happens to the potential energy if the charge is doubled and the potential remains the same?

Correct Answer: A

Q24.A charge is moved from point A to point B along an equipotential surface. What is the work done by the electric field?

Correct Answer: C

Q25.What is the expression for the electric potential VVV due to a point charge QQQ at a distance rrr from the charge?

Correct Answer: A

Q26.Consider a dielectric slab placed in a uniform electric field. If the dielectric constant is KKK, how does the presence of the dielectric affect the electric field inside the slab?

Correct Answer: C

Q27.What is the potential inside a uniformly charged spherical shell?

Correct Answer: B

Correct Answer: A

Q29.A parallel plate capacitor with a dielectric constant KKK is charged to a potential VVV. If the dielectric is removed while the capacitor remains connected to the battery, what happens to the charge on the capacitor?

Correct Answer: C

Q30.For an electric dipole, the potential at a point on the equatorial plane is:

Correct Answer: C

Q31.What is the electric field just outside the surface of a charged conductor?