CBSE Class 12 · 2020 · ElectrostaticsLong Answer

(a) 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

.
(b) Draw equipotential surfaces due to an isolated point charge

(- q)

and depict the electric field lines.
(c) 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.

Solution

(a) Work to bring

q_{1}

into the external field:

W_{1} = q_{1} V (r_{1})

.
Work to bring

q_{2}

W_{2} = q_{2} V (r_{2}) + \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r _{12}}

U = q_{1} V (r_{1}) + q_{2} V (r_{2}) + \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r _{12}}

(b) For

- q

the equipotentials are concentric spheres and the field lines point radially inward.
(c) Work to assemble the three charges:

W = \frac{1}{4 π ε _{0} r} [q_{1} q_{2} + q_{2} q_{3} + q_{3} q_{1}]

W = \frac{9 \times 1 0 ^{9}}{0.1} [(1) (- 1) + (- 1) (2) + (2) (1)] \times 1 0^{- 12}

W = - 9 \times 1 0^{- 2} J

CBSE Class 12 Board · 2020 · Subjective