CBSE Class 12 Physics 2019 Delhi Set 1 Paper

Question : 13 of 27

Marks: +1, -0

SECTION -C

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

{\Z}

-direction.
(b) Derive an expression for the electric potential at any point along the axial line of an electric dipole.

Solution:

(a)Drawing of equipotential surfaces
(b) Derivation of the expression of electric potential

(b)

Potential at point

P

\; {\V} p= {\V}-q+ {\V}+q

\;=\;{1}/{4 π ε_0} \;{-q}/{(r+a)}+\;{1}/{4 π ε_0} \;{q}/{(r-a)}

\;=\;{q}/{4 π ε_0} [\;{1}/{(r-a)}-\;{1}/{(r+a)}]

\;=\;{q}/{4 π ε_0} [\;{r+a-r+a}/{(r-a)(r+a)}]

\;=\;{q}/{4 π ε_0} × \;{2 a}/{ (r^2-a^2) }=\;{q × 2 a}/{4 π ε_0 (r^2-a^2) }

\;=\;{1}/{4 π ε_0} \;{p}/{ (r^2-a^2) }

where,

p

is the dipole moment.

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