Question 1

Consider a dipole with charges $+q$ and $-q$ separated by a distance $d$. What is the expression for the electric field at a point on the axial line at a distance $r$ from the center of the dipole, assuming $r \gg d$?

Accepted Answer

Correct Option: A. Solution: For a dipole on the axial line, the electric field is given by $E = \frac{1}{4\pi\varepsilon_0} \frac{2qd}{r^3}$, where $r \gg d$. This is derived using the dipole approximation.

Question 2

What is the nature of the force between two charges of opposite signs according to Coulomb's Law?

Accepted Answer

Correct Option: B. Solution: Coulomb's Law states that the force between two charges is attractive if the charges have opposite signs.

Question 3

Consider a closed surface with an electric field passing through it. If the electric field is uniform and the surface is oriented such that the angle between the field and the normal to the surface is $30^{\circ}$, what is the electric flux through the surface if the area of the surface is $2 \ m^2$ and the magnitude of the electric field is $5 \ N/C$?

Accepted Answer

Correct Option: C. Solution: The electric flux $\Phi$ through a surface is given by $\Phi = E \cdot S \cdot \cos	heta$, where $E$ is the electric field, $S$ is the area, and $	heta$ is the angle between the field and the normal to the surface. Substituting the given values: $\Phi = 5 \ N/C 	imes 2 \ m^2 	imes \cos(30^{\circ}) = 10 	imes \frac{\sqrt{3}}{2} = 8.66 \ N \cdot m^2/C$.

Question 4

Which of the following materials is an insulator?

Accepted Answer

Correct Option: B. Solution: Glass is an insulator because it does not allow charges to move freely.

Question 5

According to the superposition principle, what is the total force on a charge when multiple charges are present?

Accepted Answer

Correct Option: B. Solution: The superposition principle states that the total force on a charge is the vector sum of the forces exerted by other individual charges.

Question 6

A student claims that the electric field due to an infinite plane sheet of charge decreases with distance. Evaluate this statement.

Accepted Answer

Correct Option: B. Solution: The electric field due to an infinite plane sheet of charge is constant and given by $E = \frac{\sigma}{2\varepsilon_0}$, independent of the distance from the sheet. Therefore, the statement is incorrect.

Question 7

Consider a continuous charge distribution along a line of length $L$ with a uniform linear charge density $\lambda$. What is the expression for the electric field at a point $P$ located at a perpendicular distance $d$ from the midpoint of the line?

Accepted Answer

Correct Option: A. Solution: The electric field due to a continuous charge distribution is calculated by integrating the contributions from each infinitesimal charge element. For a line charge, the electric field at a point perpendicular to the midpoint is given by $E = \frac{1}{4\pi\varepsilon_0} \cdot \frac{2\lambda L}{d\sqrt{d^2 + (L/2)^2}}$.

Question 8

Consider two point charges, $q_1 = +2 	imes 10^{-6} 	ext{ C}$ and $q_2 = -3 	imes 10^{-6} 	ext{ C}$, placed 0.1 m apart in vacuum. Calculate the magnitude of the force between them using Coulomb's law.

Accepted Answer

Correct Option: C. Solution: Using Coulomb's law, $$F = \frac{k |q_1 q_2|}{r^2}$$ where $k = 9 	imes 10^9 	ext{ Nm}^2/	ext{C}^2$, $q_1 = 2 	imes 10^{-6} 	ext{ C}$, $q_2 = 3 	imes 10^{-6} 	ext{ C}$, and $r = 0.1 	ext{ m}$. $$F = \frac{9 	imes 10^9 	imes 2 	imes 10^{-6} 	imes 3 	imes 10^{-6}}{(0.1)^2} = 4.5 	ext{ N}$$.

Question 9

Consider a system of three point charges $q_1 = +2e$, $q_2 = -3e$, and $q_3 = +4e$. What is the total charge of the system?

Accepted Answer

Correct Option: D. Solution: The total charge of the system is the algebraic sum of all individual charges: $q_{total} = q_1 + q_2 + q_3 = +2e - 3e + 4e = +3e$. However, this was a trick question as the correct total charge should be calculated as $+3e$.

Question 10

Consider a dipole placed in a non-uniform electric field. Which of the following outcomes is possible?

Accepted Answer

Correct Option: C. Solution: In a non-uniform electric field, a dipole can experience both a net force and a torque. The force depends on the gradient of the electric field and the orientation of the dipole.

Question 11

What is the expression for electric flux through an area element when the electric field is at an angle $	heta$ with the normal to the surface?

Accepted Answer

Correct Option: A. Solution: Electric flux $\Phi$ through an area element is given by $\Phi = E \cdot S \cdot \cos 	heta$, where $E$ is the electric field, $S$ is the area, and $	heta$ is the angle between the field and the normal to the surface.

Question 12

Consider a point charge $Q$ placed at the origin. If another charge $q$ is placed at a point $P$ at a distance $r$ from $Q$, which of the following correctly describes the electric field $E$ at point $P$?

Accepted Answer

Correct Option: A. Solution: The electric field $E$ due to a point charge $Q$ at a distance $r$ is given by $E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r^2}$ and is directed radially outward if $Q$ is positive and radially inward if $Q$ is negative.

Question 13

Consider a closed surface with a net electric flux of zero. Which of the following statements is true about the charges inside the surface?

Accepted Answer

Correct Option: B. Solution: A net electric flux of zero through a closed surface indicates that the net enclosed charge is zero. However, there can still be positive and negative charges inside the surface that cancel each other out.

Question 14

A point charge $Q = 5\, \mu C$ is placed at the origin. Calculate the electric field at a point $P(0.2, 0, 0)\, m$ due to this charge.

Accepted Answer

Correct Option: B. Solution: The electric field due to a point charge is given by $E = \frac{kQ}{r^2}$. Here, $r = 0.2\, m$, so $E = \frac{9 	imes 10^9 	imes 5 	imes 10^{-6}}{(0.2)^2} = 2.25 	imes 10^6\, N/C$ directed along the x-axis.

Question 15

What is the direction of the electric field produced by a positive point charge?

Accepted Answer

Correct Option: A. Solution: The electric field produced by a positive point charge is directed radially outward from the charge.

Question 16

A cylindrical Gaussian surface of radius $r$ and length $L$ is placed around an infinitely long uniformly charged wire with linear charge density $\lambda$. What is the total electric flux through the cylindrical surface?

Accepted Answer

Correct Option: A. Solution: According to Gauss's Law, the total electric flux $\Phi$ through a closed surface is $\Phi = \frac{Q_{enc}}{\varepsilon_0}$, where $Q_{enc}$ is the charge enclosed by the surface. For a cylindrical surface around an infinitely long wire, $Q_{enc} = \lambda L$. Thus, the total electric flux is $\Phi = \frac{\lambda L}{\varepsilon_0}$.

Question 17

What is the direction of the dipole moment in an electric dipole consisting of charges $+q$ and $-q$ separated by a distance $2a$?

Accepted Answer

Correct Option: B. Solution: The dipole moment $\mathbf{p} = q 	imes 2a$ is directed from the negative charge to the positive charge.

Question 18

Consider two point charges, $q_1 = +2 	imes 10^{-8} \, C$ and $q_2 = -2 	imes 10^{-8} \, C$, placed 0.2 m apart in vacuum. If a third charge $q_3 = +1 	imes 10^{-8} \, C$ is placed at the midpoint of the line joining $q_1$ and $q_2$, what is the net force experienced by $q_3$?

Accepted Answer

Correct Option: A. Solution: The electric forces due to $q_1$ and $q_2$ on $q_3$ are equal in magnitude and opposite in direction, thus canceling each other out. Therefore, the net force on $q_3$ is zero.

Question 19

According to Coulomb's law, what is the force between two point charges $q_1$ and $q_2$ separated by a distance $r$ in a vacuum?

Accepted Answer

Correct Option: A. Solution: Coulomb's law states that the force between two point charges $q_1$ and $q_2$ separated by a distance $r$ is given by $F = k \frac{q_1 q_2}{r^2}$, where $k$ is the Coulomb's constant.

Question 20

If a system contains three point charges $q_1 = +2e$, $q_2 = -3e$, and $q_3 = +4e$, what is the total charge of the system?

Accepted Answer

Correct Option: D. Solution: The total charge of the system is the algebraic sum of the individual charges: $q_1 + q_2 + q_3 = +2e - 3e + 4e = +1e$.

Question 21

Consider a metal sphere connected to the ground by a conducting wire. If a negatively charged rod is brought close to the sphere without touching it, what happens to the charge distribution on the sphere?

Accepted Answer

Correct Option: D. Solution: When the negatively charged rod is brought near, electrons on the sphere are repelled and move to the ground through the conducting wire, leaving the sphere with a positive charge.

Question 22

Which of the following statements about electric charge is true?

Accepted Answer

Correct Option: B. Solution: The principle of conservation of charge states that the total charge of an isolated system remains constant. Charge is neither created nor destroyed, and it exists in integral multiples of $e$.

Question 23

Consider a point charge $Q$ placed at the origin. If another point charge $q$ is placed at a distance $r$ from $Q$, the electric field experienced by $q$ is given by which of the following expressions?

Accepted Answer

Correct Option: A. Solution: The electric field due to a point charge $Q$ at a distance $r$ is given by $E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r^2}$, where $\varepsilon_0$ is the permittivity of free space.

Question 24

According to Gauss's Law, the total electric flux through a closed surface is equal to which of the following?

Accepted Answer

Correct Option: A. Solution: Gauss's Law states that the total electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space, $\varepsilon_0$.

Question 25

In an isolated system, two charges are initially $q_1 = +5e$ and $q_2 = -5e$. After some time, charge is transferred between them such that $q_1 = +3e$. What is the final charge on $q_2$?

Accepted Answer

Correct Option: B. Solution: The principle of conservation of charge states that the total charge of an isolated system remains constant. Initially, the total charge is $+5e + (-5e) = 0$. After charge transfer, $q_1 = +3e$, so $q_2$ must be $-3e$ to maintain the total charge at $0$. However, the correct calculation should have been $q_2 = -7e$.

Question 26

Consider three charges $q_1$, $q_2$, and $q_3$ placed at the vertices of an equilateral triangle. What is the force on a charge $Q$ placed at the centroid of the triangle?

Accepted Answer

Correct Option: A. Solution: In an equilateral triangle with charges at the vertices, the forces due to each charge on a charge $Q$ at the centroid cancel out due to symmetry, resulting in a net force of zero.

Question 27

Consider a cylindrical Gaussian surface surrounding an infinitely long uniformly charged wire. If the radius of the cylindrical surface is doubled, how does the electric field at the surface change?

Accepted Answer

Correct Option: C. Solution: The electric field due to an infinitely long uniformly charged wire is inversely proportional to the distance from the wire, $E = \frac{\lambda}{2\pi \varepsilon_0 r}$. Doubling the radius of the Gaussian surface halves the electric field.

Question 28

In which direction does the electric field due to a dipole point on the equatorial line?

Accepted Answer

Correct Option: B. Solution: The electric field due to a dipole on the equatorial line points perpendicular to the dipole axis.

Question 29

Consider three point charges $q_1 = +2\, \mu C$, $q_2 = -2\, \mu C$, and $q_3 = +2\, \mu C$ placed at the vertices of an equilateral triangle with side length $0.1\, m$. What is the magnitude of the electric field at the centroid of the triangle?

Accepted Answer

Correct Option: A. Solution: The electric field at the centroid due to the symmetrical arrangement of charges cancels out. Therefore, the net electric field is $0\, N/C$.

Question 30

Which of the following correctly describes the behavior of the electric field due to a dipole at a point on the equatorial line?

Accepted Answer

Correct Option: B. Solution: For a dipole, the electric field on the equatorial line is directed perpendicular to the line joining the charges and points from positive to negative charge.

Question 31

A rod of length $L$ has a linear charge density $\lambda(x) = \lambda_0 \frac{x}{L}$, where $x$ is the distance from one end of the rod. What is the electric field at a point $P$ located at a distance $d$ from the end of the rod along its perpendicular bisector?

Accepted Answer

Correct Option: B. Solution: The electric field due to a non-uniform charge distribution requires integrating the contributions from each infinitesimal charge element. For the given linear charge density $\lambda(x) = \lambda_0 \frac{x}{L}$, the electric field at point $P$ is $E = \frac{\lambda_0}{4\pi\varepsilon_0} \cdot \frac{L^2}{d\sqrt{d^2 + L^2}}$.

Question 32

For an infinitely long uniformly charged wire, the electric field at a distance $r$ from the wire is given by which of the following expressions?

Accepted Answer

Correct Option: A. Solution: The electric field due to an infinitely long uniformly charged wire is radial and has a magnitude given by $E = \frac{\lambda}{2\pi \varepsilon_0 r}$, where $\lambda$ is the linear charge density.

Question 33

Which of the following statements is true regarding a Gaussian surface?

Accepted Answer

Correct Option: A. Solution: A Gaussian surface is chosen based on symmetry to simplify calculations by ensuring the electric field is constant or has a simple orientation over parts of the surface. It should not pass through a discrete point charge.

Question 34

Which of the following statements about the quantization of electric charge is correct?

Accepted Answer

Correct Option: B. Solution: The quantization of charge means that the charge $q$ on a body is always an integral multiple of the elementary charge $e$, i.e., $q = ne$, where $n$ is an integer. This is a fundamental property of electric charge.

Question 35

Which of the following statements about electric field lines is incorrect?

Accepted Answer

Correct Option: B. Solution: Electric field lines can never intersect each other because at the point of intersection, the field would have two different directions, which is not possible.

Question 36

A Gaussian surface is chosen such that it encloses a point charge $+Q$. If the Gaussian surface is a sphere centered at the charge, what is the electric flux through the surface?

Accepted Answer

Correct Option: A. Solution: According to Gauss's law, the electric flux through a closed surface enclosing a charge $Q$ is given by $\frac{Q}{\varepsilon_0}$. Since the Gaussian surface is a sphere centered at the charge, it encloses the entire charge $+Q$.

Question 37

Two charges, $+q$ and $-q$, are placed at a distance $d$ apart. What is the electric field at the midpoint between the charges?

Accepted Answer

Correct Option: A. Solution: At the midpoint between two equal and opposite charges, the electric fields due to each charge are equal in magnitude but opposite in direction, thus canceling each other out. Therefore, the net electric field is zero.

Question 38

A cube with side length $a$ is placed in a uniform electric field $E$. The field is parallel to one of the cube's faces. What is the net electric flux through the cube?

Accepted Answer

Correct Option: B. Solution: In a uniform electric field, the number of field lines entering a closed surface is equal to the number leaving, resulting in a net flux of zero through the surface.

Question 39

Which of the following scenarios best illustrates the application of Gauss's Law?

Accepted Answer

Correct Option: B. Solution: Gauss's Law is particularly useful for calculating the electric field in cases of high symmetry, such as inside a uniformly charged spherical shell.

Question 40

How does the superposition principle apply to the force on a charge $q_1$ due to other charges $q_2$ and $q_3$?

Accepted Answer

Correct Option: C. Solution: According to the superposition principle, the force on a charge $q_1$ due to other charges $q_2$ and $q_3$ is the vector sum of the forces from $q_2$ and $q_3$, considering their directions.

Question 41

How does a dipole behave in a non-uniform electric field?

Accepted Answer

Correct Option: B. Solution: In a non-uniform electric field, a dipole can experience a net force depending on its orientation with respect to the field.

Question 42

Consider an infinitely long uniformly charged wire with linear charge density $\lambda$. If the electric field at a distance $r$ from the wire is given by $E = \frac{\lambda}{2\pi\varepsilon_0 r}$, what will be the electric field at a distance $2r$ from the wire?

Accepted Answer

Correct Option: C. Solution: The electric field due to an infinitely long uniformly charged wire is inversely proportional to the distance from the wire. Therefore, at a distance $2r$, the electric field is $E = \frac{\lambda}{2\pi\varepsilon_0 	imes 2r}$.

Question 43

A proton and an electron are placed in a uniform electric field. Which statement correctly describes their motion?

Accepted Answer

Correct Option: B. Solution: In a uniform electric field, a proton will accelerate in the direction of the field due to its positive charge, while an electron will accelerate in the opposite direction due to its negative charge.

Question 44

Consider a Gaussian surface enclosing a charge distribution. Which of the following is a correct application of Gauss's Law?

Accepted Answer

Correct Option: A. Solution: Gauss's Law states that the net electric flux through a closed surface is proportional to the enclosed charge. If the enclosed charge is zero, the net electric flux is also zero, regardless of the shape of the Gaussian surface.

Question 45

What is the electric field at a point due to multiple charges according to the superposition principle?

Accepted Answer

Correct Option: A. Solution: The electric field at a point due to multiple charges is the vector sum of the fields due to each charge, calculated using the superposition principle.

Question 46

If the distance between two charges is doubled, how does the electrostatic force between them change?

Accepted Answer

Correct Option: B. Solution: According to Coulomb's law, the force between two charges is inversely proportional to the square of the distance between them. If the distance is doubled, the force becomes one-fourth of its original value.

Question 47

For an infinite plane sheet of uniform surface charge density $\sigma$, what is the magnitude of the electric field $E$ at a point near the sheet?

Accepted Answer

Correct Option: A. Solution: The electric field due to an infinite plane sheet of uniform surface charge density $\sigma$ is given by $E = \frac{\sigma}{2\varepsilon_0}$, and it is independent of the distance from the sheet.

Question 48

Consider an infinite plane sheet with a uniform surface charge density $\sigma$. According to Gauss's Law, what is the magnitude of the electric field at a point located at a distance $d$ from the sheet?

Accepted Answer

Correct Option: A. Solution: For an infinite plane sheet of uniform surface charge density, the electric field is given by $E = \frac{\sigma}{2\varepsilon_0}$ and is independent of the distance $d$ from the sheet.

Question 49

Consider a closed surface enclosing a charge $q$. According to Gauss's Law, which of the following statements is true about the electric flux through the surface?

Accepted Answer

Correct Option: B. Solution: According to Gauss's Law, the total electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space, i.e., $$\Phi = \frac{q_{	ext{enclosed}}}{\varepsilon_0}$$. This is independent of the shape or size of the surface.

Question 50

When can charged bodies be treated as point charges?

Accepted Answer

Correct Option: B. Solution: Charged bodies can be treated as point charges when their size is much smaller than the separation between them, allowing the charge to be considered as concentrated at a single point.

Question 51

What is the dependence of the electric field due to a dipole on the axial line at a far distance?

Accepted Answer

Correct Option: B. Solution: The electric field due to a dipole on the axial line at a far distance depends on $1/r^3$, unlike the $1/r^2$ dependence for a point charge.

Question 52

What does zero electric flux through a closed surface indicate about the enclosed charge?

Accepted Answer

Correct Option: B. Solution: Zero electric flux through a closed surface indicates that the net enclosed charge is zero, regardless of the shape of the surface or external charges.

Question 53

A spherical shell of radius $R$ encloses a point charge $+Q$ at its center. If another charge $-Q$ is placed outside the shell, what is the net electric flux through the shell?

Accepted Answer

Correct Option: B. Solution: According to Gauss's Law, the electric flux through a closed surface depends only on the charge enclosed within the surface. The external charge does not affect the flux through the shell, so the net flux is $$\frac{Q}{\varepsilon_0}$$.

Question 54

Consider a charged comb attracting small bits of paper. Which of the following best explains this phenomenon?

Accepted Answer

Correct Option: B. Solution: The charged comb induces a dipole moment in the neutral paper. The non-uniform electric field of the comb causes the paper to be attracted due to the induced dipole interaction.

Question 55

For a uniformly charged thin spherical shell, what is the electric field inside the shell?

Accepted Answer

Correct Option: A. Solution: According to Gauss's Law, the electric field inside a uniformly charged thin spherical shell is zero.

Question 56

A charge $q$ is placed at the center of a cube. What is the electric flux through one face of the cube?

Accepted Answer

Correct Option: A. Solution: By Gauss's law, the total electric flux through the cube is $\frac{q}{\varepsilon_0}$. Since the cube has six faces, the flux through one face is $\frac{q}{6\varepsilon_0}$.

Question 57

A uniformly charged thin spherical shell has a charge $Q$. What is the electric field at a point $P$ inside the shell?

Accepted Answer

Correct Option: A. Solution: According to Gauss's Law, the electric field inside a uniformly charged thin spherical shell is zero.

Question 58

Which of the following statements correctly explains the behavior of a charged comb attracting small pieces of paper?

Accepted Answer

Correct Option: B. Solution: A charged comb attracts small pieces of paper by inducing a temporary dipole moment in the paper due to the non-uniform electric field created by the comb.

Question 59

What is the principle used to calculate the electric field due to a continuous charge distribution?

Accepted Answer

Correct Option: A. Solution: The electric field due to a continuous charge distribution is obtained by dividing the charge into small elements and summing or integrating their contributions using Coulomb’s law and the superposition principle.

Question 60

A cube of side $a = 0.1 	ext{ m}$ is placed in a uniform electric field $E = 3 	imes 10^4 	ext{ N/C}$ directed along the positive z-axis. Calculate the electric flux through the cube.

Accepted Answer

Correct Option: B. Solution: The electric flux through the cube is given by $\Phi = E \cdot A = E \cdot a^2$. Since the field is uniform and perpendicular to the top and bottom faces, $\Phi = 3 	imes 10^4 	imes (0.1)^2 = 3 	imes 10^2 	ext{ Nm}^2/	ext{C}$.

Question 61

If the electric field at a point due to a point charge is $3 	imes 10^5 	ext{ N/C}$, what will be the electric field at a point twice as far from the charge?

Accepted Answer

Correct Option: A. Solution: The electric field due to a point charge varies inversely with the square of the distance. If the distance is doubled, the electric field becomes one-fourth. Therefore, the new electric field is $\frac{3 	imes 10^5}{4} = 7.5 	imes 10^4 	ext{ N/C}$.

Question 62

If a rod has a linear charge density $\lambda = 5 	imes 10^{-6} C/m$, what is the total charge on a 2-meter section of the rod?

Accepted Answer

Correct Option: A. Solution: The total charge $Q$ on a section of the rod is given by $Q = \lambda 	imes L = 5 	imes 10^{-6} C/m 	imes 2 m = 1 	imes 10^{-5} C$.

Question 63

In a system of charges, which statement about the principle of superposition is correct?

Accepted Answer

Correct Option: B. Solution: The principle of superposition states that the net force on a charge due to a system of other charges is the vector sum of individual forces exerted by each charge. This means that each force is considered with its magnitude and direction, and they are added using vector addition.

Question 64

If the dipole moment of an electric dipole is doubled while keeping the distance between charges constant, how does the electric field at a point on the perpendicular bisector of the dipole change?

Accepted Answer

Correct Option: B. Solution: The electric field on the perpendicular bisector of a dipole is directly proportional to the dipole moment $p$. Therefore, if the dipole moment is doubled, the electric field also doubles.

Electric Charges and Fiel..

Learning Objectives

Revision Notes & Summary

Chapter One: Electric Charges and Fields

1.1 Introduction

1.2 Electric Charge

1.3 Basic Properties of Electric Charge

1.4 Conductors and Insulators

1.5 Coulomb's Law

1.6 Electric Field and Electric Flux

1.7 Electric Dipole

1.8 Important Concepts

1.9 Exercises

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Exam Tips

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Multiple Choice Questions

Q1.Consider a dipole with charges +q+q+q and −q-q−q separated by a distance ddd. What is the expression for the electric field at a point on the axial line at a distance rrr from the center of the dipole, assuming r≫dr \gg dr≫d?

Correct Answer: A

Q2.What is the nature of the force between two charges of opposite signs according to Coulomb's Law?

Correct Answer: B

Correct Answer: C

Q4.Which of the following materials is an insulator?

Correct Answer: B

Q5.According to the superposition principle, what is the total force on a charge when multiple charges are present?

Correct Answer: B

Q6.A student claims that the electric field due to an infinite plane sheet of charge decreases with distance. Evaluate this statement.

Correct Answer: B

Q7.Consider a continuous charge distribution along a line of length LLL with a uniform linear charge density λ\lambdaλ. What is the expression for the electric field at a point PPP located at a perpendicular distance ddd from the midpoint of the line?

Correct Answer: A

Q8.Consider two point charges, q1=+2×10−6 Cq_1 = +2 \times 10^{-6} \text{ C}q1​=+2×10−6 C and q2=−3×10−6 Cq_2 = -3 \times 10^{-6} \text{ C}q2​=−3×10−6 C, placed 0.1 m apart in vacuum. Calculate the magnitude of the force between them using Coulomb's law.

Correct Answer: C

Q9.Consider a system of three point charges q1=+2eq_1 = +2eq1​=+2e, q2=−3eq_2 = -3eq2​=−3e, and q3=+4eq_3 = +4eq3​=+4e. What is the total charge of the system?

Correct Answer: D

Q10.Consider a dipole placed in a non-uniform electric field. Which of the following outcomes is possible?

Correct Answer: C

Q11.What is the expression for electric flux through an area element when the electric field is at an angle θ\thetaθ with the normal to the surface?

Correct Answer: A

Q12.Consider a point charge QQQ placed at the origin. If another charge qqq is placed at a point PPP at a distance rrr from QQQ, which of the following correctly describes the electric field EEE at point PPP?

Correct Answer: A

Q13.Consider a closed surface with a net electric flux of zero. Which of the following statements is true about the charges inside the surface?

Correct Answer: B

Q14.A point charge Q=5 μCQ = 5\, \mu CQ=5μC is placed at the origin. Calculate the electric field at a point P(0.2,0,0) mP(0.2, 0, 0)\, mP(0.2,0,0)m due to this charge.

Correct Answer: B

Q15.What is the direction of the electric field produced by a positive point charge?

Correct Answer: A

Q16.A cylindrical Gaussian surface of radius rrr and length LLL is placed around an infinitely long uniformly charged wire with linear charge density λ\lambdaλ. What is the total electric flux through the cylindrical surface?

Correct Answer: A

Q17.What is the direction of the dipole moment in an electric dipole consisting of charges +q+q+q and −q-q−q separated by a distance 2a2a2a?

Correct Answer: B

Correct Answer: A

Q19.According to Coulomb's law, what is the force between two point charges q1q_1q1​ and q2q_2q2​ separated by a distance rrr in a vacuum?

Correct Answer: A

Q20.If a system contains three point charges q1=+2eq_1 = +2eq1​=+2e, q2=−3eq_2 = -3eq2​=−3e, and q3=+4eq_3 = +4eq3​=+4e, what is the total charge of the system?

Correct Answer: D

Q21.Consider a metal sphere connected to the ground by a conducting wire. If a negatively charged rod is brought close to the sphere without touching it, what happens to the charge distribution on the sphere?

Correct Answer: D

Q22.Which of the following statements about electric charge is true?

Correct Answer: B

Q23.Consider a point charge QQQ placed at the origin. If another point charge qqq is placed at a distance rrr from QQQ, the electric field experienced by qqq is given by which of the following expressions?

Correct Answer: A

Q24.According to Gauss's Law, the total electric flux through a closed surface is equal to which of the following?

Correct Answer: A

Q25.In an isolated system, two charges are initially q1=+5eq_1 = +5eq1​=+5e and q2=−5eq_2 = -5eq2​=−5e. After some time, charge is transferred between them such that q1=+3eq_1 = +3eq1​=+3e. What is the final charge on q2q_2q2​?

Correct Answer: B

Q26.Consider three charges q1q_1q1​, q2q_2q2​, and q3q_3q3​ placed at the vertices of an equilateral triangle. What is the force on a charge QQQ placed at the centroid of the triangle?

Correct Answer: A

Q27.Consider a cylindrical Gaussian surface surrounding an infinitely long uniformly charged wire. If the radius of the cylindrical surface is doubled, how does the electric field at the surface change?

Correct Answer: C

Q28.In which direction does the electric field due to a dipole point on the equatorial line?

Correct Answer: B

Correct Answer: A