Find the expression for the potential energy of a system of two point charges q 1 and q 2 located at r → 1 and r → 2 respectively in an external electric field E → .

Let V r 1 → and V r → 2 be the potential at r 1 → and r 2 → . Work done in bringing the first charge from infinity in the electric field E → : W 1 = q 1 V r → 1 .....(i) The total work done in bringing the charge q 2 from infinity to r → 2 will be against the electric field E → and against the field due to q 1 . The work done on q 2 against the external field: W 2 = q 2 V r → 2 .....(ii) Work done on q 2 against the field due to q 1 : W 3 = q 1 q 2 4 π ε o r 12 ......(iii) where r 12 is the distance between q 1 and q 2 . Hence, the total work done on the system of charges: W = W 1 + W 2 + W 3 = q 1 V r → 1 + q 2 V r → 2 + q 1 q 2 4 π ε o r 12 This external work done will be stored as the potential energy of the system. Hence, the required expression for the potential energy of the system: P . E . = q 1 V r → 1 + q 2 V r → 2 + q 1 q 2 4 πε o r 12

Three-point charges q , – 4 q and 2 q are placed at the vertices of an equilateral triangle ABC of side l as shown in the figure. Find out the amount of the work done to separate the charges at infinite distance.

The work done to separate the charges to infinity = Change in the potential energy of the system ⇒ W = ∆ P . E . = U f - U i The initial potential energy of the system, U i = 1 4 πε 0 ( - 4 q ) ( 2 q ) l + ( 2 q ) ( q ) l + ( - 4 q ) ( q ) l U i = q 2 4 πε 0 - 8 + 2 - 4 l = - 10 q 2 4 πε 0 l Final potential energy, U f = 0 Work done, W = U f - U i = 0 - - 10 q 2 4 πε 0 l = 10 q 2 4 πε 0 l Thus, W = 5 q 2 2 πε 0 l

Four-point charges Q , q , Q and q are placed at the corners of a square of side ' a ' as shown in the figure. Find the potential energy of this system.

The potential energy between two charges q 1 and q 2 separated by a distance can be given as U = 1 4 πε 0 q 1 q 2 r From the diagram, the adjacent charges are kept at equal distances. Thus, by symmetry, the system potential energy between charges that are adjacent to each other will be the same, and it can be given as: U 1 = 4 × 1 4 πε 0 q Q a For the diagonally opposite charge q , the Potential energy will be: U 2 = 1 4 πε 0 q 2 a 2 For the diagonally opposite charge Q , the potential energy will be: U 3 = 1 4 πε 0 Q 2 a 2 Thus, the total potential energy of the system, U = U 1 + U 2 + U 3 U = 4 × 1 4 πε 0 q Q a + 1 4 πε 0 q 2 a 2 + 1 4 πε 0 Q 2 a 2 U = 1 4 πε 0 a 4 q Q + q 2 2 + Q 2 2

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Draw the equipotential surfaces corresponding to a uniform electric field in the $z ‐$ direction.

Important Questions on Electrostatic Potential and Capacitance

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12th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 2 - Electrostatic Potential and Capacitance>cbse-2019>Q 4

Derive an expression for the electric potential at any point along the axial line of an electric dipole.

EASY

12th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 2 - Electrostatic Potential and Capacitance>cbse-2019>Q 5

Describe briefly the process of transferring the charge between the two plates of a parallel plate capacitor when connected to a battery. Derive an expression for the energy stored in a capacitor.

MEDIUM

12th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 2 - Electrostatic Potential and Capacitance>cbse-2019>Q 6

A parallel plate capacitor is charged by a battery to a potential difference V. It is disconnected from battery and then connected to another uncharged capacitor of the same capacitance. Calculate the ratio of the energy stored in the combination to the initial energy on the single capacitor.

MEDIUM

12th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 2 - Electrostatic Potential and Capacitance>cbse-2020>Q 7

The space between the plates of a parallel plate capacitor is completely filled in two ways. In the first case, it is filled with a slab of dielectric constant $K$ . In the second case, it is filled with two slabs of equal thickness and dielectric constants $K_{1}$ and $K_{2}$ respectively as shown in the figure. The capacitance of the capacitor is same in the two cases. Obtain the relationship between $K$ , $K_{1}$ and $K_{2}$ .

Question Image

MEDIUM

12th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 2 - Electrostatic Potential and Capacitance>cbse-2020>Q 8

Find the expression for the potential energy of a system of two point charges

q_{1}

and

q_{2}

located at

{\vec{r}}_{1}

and

{\vec{r}}_{2}

respectively in an external electric field

\vec{E}

EASY

12th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 2 - Electrostatic Potential and Capacitance>cbse-2020>Q 9

Draw equipotential surface due to an isolated point charge $(- q)$ and depict the electric field lines.

MEDIUM

12th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 2 - Electrostatic Potential and Capacitance>cbse-2020>Q 10

Three point charges $+ 1 μ C, - 1 μ C$ and $+ 2 μ C$ are initially infinite distance apart. Calculate the work done in assembling these charges at the vertices of an equilateral triangle of side $10 cm$ . Take $(\frac{1}{4 π ε_{o}}) = 9 \times 10^{9} N m^{2} C^{- 2}$

Draw the equipotential surfaces corresponding to a uniform electric field in the z‐direction.

Important Questions on Electrostatic Potential and Capacitance

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Draw the equipotential surfaces corresponding to a uniform electric field in the $z ‐$ direction.