CBSE Class 12 · 2010 · ElectrostaticsShort Answer

(a) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance

d

apart.
(b) Deduce the expression for the potential energy of a system of two point charges

q_{1}

and

q_{2}

brought from infinity to the points

r_{1}

and

r_{2}

respectively in the presence of an external electric field

E

Solution

(a) Around each positive charge the equipotentials are closed surfaces; midway they are pushed apart, giving a symmetric two-lobe pattern.
(b) Work to bring

q_{1}

from infinity to

r_{1}

against the external field:

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

Work to bring

q_{2}

r_{2}

, against the external field and the field of

q_{1}

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

Total potential energy:

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

CBSE Class 12 Board · 2010 · Subjective

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CBSE Class 12 · 2010 · ElectrostaticsShort Answer

Solution

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