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 + 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 1 4 π ε o = 9 × 10 9 N m 2 C - 2

A possible configuration of the three charges is shown below. No external field is present and, the charges are initially infinite distance apart. Hence, the work done in bringing the first charge + 1 μC at A from infinity will be zero. W 1 = 0 .....(i) The potential at point B due to the first charge + 1 μC , at a distance of 10 cm , from the charge A: V 1 = 9 × 10 9 × 1 × 10 - 6 10 × 10 - 2 = 9 × 10 4 J / C Work done in bringing - 1 μC charge at point B: W 2 = - 1 × 10 - 6 × 9 × 10 4 = - 9 × 10 - 2 J .....(ii) The potential at point C due to the charge present at A: V 2 = 9 × 10 4 J / C The potential at point C due to the charge present at B: V 3 = 9 × 10 9 × - 1 × 10 - 6 10 × 10 - 2 = - 9 × 10 4 J / C The work done on + 2 μ C will be due to two charges that are already present. The total work done on it: W 3 = Work done due to charge present at A+ Work done due to the charge present at B W 3 = 2 × 9 × 10 4 + 2 × - 9 × 10 4 = 0 The total work done in assembling the three given charges, as shown in the above diagram: W 1 + W 2 + W 3 = - 9 × 10 4 J The work-done in assembling the three charges will be - 9 × 10 4 J .

MEDIUM

12th CBSE

IMPORTANT

Earn 100

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.

Important Questions on Electrostatic Potential and Capacitance

MEDIUM

12th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 2 - Electrostatic Potential and Capacitance>cbse-2018>Q 2

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.

Question Image

MEDIUM

12th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 2 - Electrostatic Potential and Capacitance>cbse-2019>Q 3

Draw the equipotential surfaces corresponding to a uniform electric field in the

z ‐

direction.

HARD

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.

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.

Important Questions on Electrostatic Potential and Capacitance

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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.