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Physics Part 1

Electrostatic Potential and Capacitance

Electrostatic Potential and Capacitance

Action PlanNotesQuestionsMock-Test
Study Action Plan (Sorted by Difficulty)
Energy Density of Electric Field
Accuracy: 0%
Total Attempted0
Total Correct0
Total Incorrect0
Difficulty Level:
High
Energy Stored in Capacitor
Accuracy: 20%
Total Attempted10
Total Correct2
Total Incorrect8
Difficulty Level:
High
Polar and Non-polar Dielectrics
Accuracy: 20%
Total Attempted5
Total Correct1
Total Incorrect4
Difficulty Level:
High
Electron Volt and Energy from Potential Difference
Accuracy: 29%
Total Attempted7
Total Correct2
Total Incorrect5
Difficulty Level:
High
Potential of Uniformly Charged Spherical Shell
Accuracy: 30%
Total Attempted10
Total Correct3
Total Incorrect7
Difficulty Level:
High
Electrostatic Potential and Potential Difference
Accuracy: 33%
Total Attempted24
Total Correct8
Total Incorrect16
Difficulty Level:
High
Capacitance and Capacitors
Accuracy: 40%
Total Attempted25
Total Correct10
Total Incorrect15
Difficulty Level:
High
Electrostatic Shielding and Cavities
Accuracy: 40%
Total Attempted5
Total Correct2
Total Incorrect3
Difficulty Level:
High
Capacitors in Series
Accuracy: 43%
Total Attempted35
Total Correct15
Total Incorrect20
Difficulty Level:
High
Parallel Plate Capacitor
Accuracy: 46%
Total Attempted28
Total Correct13
Total Incorrect15
Difficulty Level:
High
Potential Due to a System of Charges
Accuracy: 47%
Total Attempted30
Total Correct14
Total Incorrect16
Difficulty Level:
High
Dielectrics and Polarization
Accuracy: 47%
Total Attempted64
Total Correct30
Total Incorrect34
Difficulty Level:
High
Electrostatics of Conductors
Accuracy: 50%
Total Attempted64
Total Correct32
Total Incorrect32
Difficulty Level:
Medium
Potential Energy of Charge in External Field
Accuracy: 53%
Total Attempted17
Total Correct9
Total Incorrect8
Difficulty Level:
Medium
Electric Dipole Potential
Accuracy: 56%
Total Attempted9
Total Correct5
Total Incorrect4
Difficulty Level:
Medium
Potential Energy of Dipole in External Electric Field
Accuracy: 56%
Total Attempted36
Total Correct20
Total Incorrect16
Difficulty Level:
Medium
Electric Field at Surface of Charged Conductor
Accuracy: 56%
Total Attempted25
Total Correct14
Total Incorrect11
Difficulty Level:
Medium
Electrostatic Potential Energy
Accuracy: 57%
Total Attempted75
Total Correct43
Total Incorrect32
Difficulty Level:
Medium
Electric Potential Due to Point Charge
Accuracy: 58%
Total Attempted52
Total Correct30
Total Incorrect22
Difficulty Level:
Medium
Dielectric Constant, Permittivity and Susceptibility
Accuracy: 61%
Total Attempted18
Total Correct11
Total Incorrect7
Difficulty Level:
Medium
Equipotential Surfaces
Accuracy: 67%
Total Attempted58
Total Correct39
Total Incorrect19
Difficulty Level:
Medium
Capacitors in Parallel
Accuracy: 69%
Total Attempted29
Total Correct20
Total Incorrect9
Difficulty Level:
Medium
Relation Between Electric Field and Potential
Accuracy: 69%
Total Attempted29
Total Correct20
Total Incorrect9
Difficulty Level:
Medium
Potential Energy of Charge Systems
Accuracy: 73%
Total Attempted52
Total Correct38
Total Incorrect14
Difficulty Level:
Medium
Effect of Dielectric on Parallel Plate Capacitor
Accuracy: 75%
Total Attempted16
Total Correct12
Total Incorrect4
Difficulty Level:
Low

Learning Objectives

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  • Learning Objectives:
    • Understand the concept of electrostatic potential and its relation to electric fields.
    • Calculate the electric potential due to point charges and charge distributions.
    • Analyze the behavior of capacitors in series and parallel configurations.
    • Apply the principles of electrostatics to solve problems involving capacitors and electric fields.
    • Explore the effects of dielectric materials on capacitance and electric fields.
    • Investigate the concept of electrostatic shielding and its applications.

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Revision Notes & Summary

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Electrostatic Potential and Capacitance

Introduction

  • The notion of potential energy was introduced in previous chapters, where work done against a force results in stored potential energy.
  • Coulomb force between stationary charges is a conservative force, similar to gravitational force.

Key Concepts

  • Electrostatic Shielding: A cavity inside a conductor is shielded from outside electrical influences, but charges inside the cavity do not shield the exterior.

Exercises

  1. Electric Potential Zero: Two charges 5 X 10⁻⁸ C and -3 X 10⁻⁸ C are located 16 cm apart. Find points where electric potential is zero.
  2. Hexagon Charge Potential: A regular hexagon with side 10 cm has a charge of 5 µC at each vertex. Calculate the potential at the center.
  3. Equipotential Surface: Two charges 2 µC and -2 µC are placed 6 cm apart. Identify an equipotential surface and the direction of the electric field on this surface.
  4. Spherical Conductor: A spherical conductor of radius 12 cm has a charge of 1.6 X 10⁻⁷C. Calculate the electric field inside, just outside, and at a point 18 cm from the center.
  5. Capacitance Calculation: A parallel plate capacitor with air has a capacitance of 8 pF. Calculate capacitance if the distance is halved and filled with a dielectric constant of 6.
  6. Series Capacitors: Three capacitors of 9 pF each are connected in series. Find total capacitance and potential difference across each capacitor connected to a 120 V supply.
  7. Parallel Capacitors: Three capacitors of 2 pF, 3 pF, and 4 pF are connected in parallel. Find total capacitance and charge on each capacitor connected to a 100 V supply.
  8. Capacitance of Parallel Plate: For a parallel plate capacitor with area 6 X 10⁻³ m² and distance 3 mm, calculate capacitance and charge when connected to a 100 V supply.

Important Formulas

  • Capacitance: C = Q/V, where Q is charge and V is potential difference.
  • Capacitance in Series: 1C=1C1+1C2+1C3+⋯\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \cdots
  • Capacitance in Parallel: C = C₁ + C₂ + C₃ + ...
  • Energy Stored in Capacitor: U = 12CV2\frac{1}{2} C V^2
  • Electric Field in Dielectric: E = E₀/K, where K is the dielectric constant.

Points to Ponder

  1. Electrostatics deals with forces between charges at rest, maintained by unspecified opposing forces.
  2. A capacitor confines electric field lines, resulting in a small potential difference despite strong fields.
  3. Electric field is zero inside a charged spherical shell, while potential is continuous across the surface.
  4. The torque on a dipole in an electric field causes oscillation, aligning with the field if damped.
  5. Potential due to a charge at its own location is infinite.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

00

B.

Q4πε0R\frac{Q}{4\pi\varepsilon_0 R}

C.

Q4πε0R−E⋅R\frac{Q}{4\pi\varepsilon_0 R} - E \cdot R

D.

E⋅RE \cdot R
Correct Answer: 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⋅RE \cdot R, where EE is the external electric field.

Chapter Concept:

Potential of Uniformly Charged Spherical Shell

A.

The electric field inside the cavity is zero.

B.

The electric field inside the cavity is equal to the field outside the conductor.

C.

The electric field inside the cavity is non-zero and varies with position.

D.

The electric field inside the cavity depends on the shape of the cavity.
Correct Answer: 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.

Chapter Concept:

Electrostatics of Conductors

A.

It increases.

B.

It decreases.

C.

It remains the same.

D.

It becomes zero.
Correct Answer: C

Solution:

The electric field EE between the plates of a capacitor is independent of the area and is given by E=VdE = \frac{V}{d}, where VV is the voltage across the plates and dd is the separation. Thus, increasing the area does not change the electric field.

Chapter Concept:

Parallel Plate Capacitor

A.

Ceq=1C1+1C2+1C3C_{eq} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}

B.

Ceq=C1+C2+C3C_{eq} = C_1 + C_2 + C_3

C.

Ceq=(1C1+1C2+1C3)−1C_{eq} = \left(\frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}\right)^{-1}

D.

Ceq=C1C2C3C_{eq} = C_1C_2C_3
Correct Answer: B

Solution:

In a parallel combination, the equivalent capacitance is the sum of the individual capacitances: Ceq=C1+C2+C3C_{eq} = C_1 + C_2 + C_3.

Chapter Concept:

Capacitors in Parallel

A.

The potential energy difference is equal to WRPW_{RP}.

B.

The potential energy difference is negative of WRPW_{RP}.

C.

The potential energy difference is independent of WRPW_{RP}.

D.

The potential energy difference is zero.
Correct Answer: 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.

Chapter Concept:

Electrostatic Potential Energy

A.

The electric field remains the same.

B.

The electric field is halved.

C.

The electric field is doubled.

D.

The electric field becomes zero.
Correct Answer: C

Solution:

The electric field in the region between the conductors is proportional to the charge QQ. Therefore, if the charge is doubled, the electric field will also be doubled.

Chapter Concept:

Capacitance and Capacitors

A.

The work done is equal to the potential energy difference between points RR and PP.

B.

The work done is zero because the electrostatic force is conservative.

C.

The work done is negative of the potential energy difference between points RR and PP.

D.

The work done is independent of the potential energy difference between points RR and PP.
Correct Answer: A

Solution:

The work done by the external force in moving a charge qq from point RR to point PP is equal to the potential energy difference between these points.

Chapter Concept:

Electrostatic Potential Energy

A.

C=C0C = C_0

B.

C=κC0C = \kappa C_0

C.

C=C0κC = \frac{C_0}{\kappa}

D.

C=C02C = \frac{C_0}{2}
Correct Answer: B

Solution:

The capacitance of a capacitor with a dielectric is given by C=κC0C = \kappa C_0, where κ\kappa is the dielectric constant.

Chapter Concept:

Capacitance and Capacitors

A.

It is zero because the work done by the external force is zero.

B.

It is equal to the work done by the external force, which is stored as potential energy.

C.

It is equal to the work done by the electric field, which is negative of the work done by the external force.

D.

It is the sum of the work done by the external force and the electric field.
Correct Answer: B

Solution:

The work done by the external force is stored as potential energy. The potential energy difference between points RR and PP is equal to the work done by the external force, which is stored as potential energy.

Chapter Concept:

Electrostatic Potential and Potential Difference

A.

The electric field inside a conductor is zero, and excess charge resides on the surface.

B.

The electric field inside a conductor is non-zero, and excess charge is uniformly distributed throughout the volume.

C.

The electric field inside a conductor is zero, but excess charge is uniformly distributed throughout the volume.

D.

The electric field inside a conductor is non-zero, and excess charge resides on the surface.
Correct Answer: 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.

Chapter Concept:

Electrostatics of Conductors

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Electrostatic Potential and Capacitance

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True or False

Correct Answer: True

Solution:

The potential energy of a system of two charges is calculated using the formula U=14πε0q1q2r12U = \frac{1}{4\pi\varepsilon_0} \frac{q_1q_2}{r_{12}}, which accounts for the interaction energy between the two charges separated by a distance r12r_{12}.

Chapter Concept :

Potential Energy of Charge Systems

Correct Answer: True

Solution:

The potential energy U=qV(r)U = qV(r) is calculated based on the external potential V(r)V(r), which is created by sources other than the charge qq itself. This ensures that the potential energy is due to the external field and not influenced by the charge's own field.

Chapter Concept :

Potential Energy of Charge in External Field

Correct Answer: True

Solution:

The expression for the potential energy of a dipole in a uniform electric field is U=−p⋅E=−pEcos⁡θU = -p \cdot E = -pE \cos \theta. Stable equilibrium occurs when the dipole moment pp is aligned with the electric field EE, meaning θ=0\theta = 0, which minimizes the potential energy.

Chapter Concept :

Potential Energy of Dipole in External Electric Field

Correct Answer: True

Solution:

The formula for electric potential due to a point charge is V=14πε0QrV = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r}, where the potential is considered zero at infinity, as stated in the provided text.

Chapter Concept :

Electric Potential Due to Point Charge

Correct Answer: True

Solution:

The capacitance CC of a capacitor is defined as the ratio C=QVC = \frac{Q}{V}, where QQ is the charge on one of the conductors and VV is the potential difference between the conductors. The capacitance depends only on the geometry of the conductors and the dielectric material between them, not on the charge or potential difference.

Chapter Concept :

Capacitance and Capacitors

Correct Answer: True

Solution:

The capacitance CC is defined as C=QVC = \frac{Q}{V}, where QQ is the charge and VV is the potential difference. It is a constant that depends only on the geometry of the conductors and the dielectric medium, not on the charge or potential difference.

Chapter Concept :

Capacitance and Capacitors

Correct Answer: True

Solution:

Dielectrics are non-conducting materials that, when placed in an external electric field, develop induced dipole moments or align existing dipoles, leading to polarization. This polarization creates bound surface charges that reduce the net electric field inside the dielectric.

Chapter Concept :

Dielectrics and Polarization

Correct Answer: True

Solution:

The potential energy of a system of charges is determined by the configuration of the charges and is independent of the path taken to assemble them, due to the conservative nature of electrostatic forces.

Chapter Concept :

Potential Energy of Charge Systems

Correct Answer: True

Solution:

This statement is true because the work done by an electrostatic field is a characteristic of a conservative force, which depends only on the initial and final positions, not the path taken.

Chapter Concept :

Electrostatic Potential Energy

Correct Answer: True

Solution:

According to the properties of a uniformly charged spherical shell, the electric field inside the shell is zero. The potential inside is constant and equal to the potential at the surface of the shell.

Chapter Concept :

Potential of Uniformly Charged Spherical Shell

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