Ncert Exercises & Solutions

An electric dipole is placed inside an arbitrary closed surface. What is the net electric flux \(\phi_E\) through the surface?
1. \(\phi_E =\dfrac{q}{\epsilon_0}\)
2. \(\phi_E =\dfrac{2q}{\epsilon_0}\)
3. \(\phi_E =\dfrac{p}{\epsilon_0 r^2}\)
4. \(\phi_E = 0\)

Hint: Use Gauss' law.

Step 1: Find the net charge inside the closed surface.

From Gauss' law, the electric flux through an enclosed surface is given by,

\oint_{s} EdS = \frac{q}{ε_{0}}

Here q is the net charge inside that enclosed surface.

Step 2: Find the flux through the surface.

Now, the net charge on a dipole is givon by, -q + q = 0

∴

The electric flux through a surface enclosing a dipole

= \frac{- q + q}{ε_{0}} = \frac{0}{ε_{0}} = 0

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