Question

A hollow insulated conduction sphere is given a positive charge of $10\mu C$. What will be the electric field at the centre of the sphere if its radius is $2m$ ?

• A. Zero
• B. $5\mu C{m}^{-2}$
• C. $20\mu C{m}^{-2}$
• D. $8\mu C{m}^{-2}$

Answer 1

Answer: (A)

Charge resides on the outer surface of a conducting hollow sphere of radius $R$.
We consider a spherical surface of radius $r<R$. By Gauss theorem
${\int }_s\vec{E}\cdot \vec{d}s=\frac{1}{{\epsilon }_0}\times$ charge enclosed or $E\times 4\pi r^2=\frac{1}{{\epsilon }_0}\times 0\Rightarrow E=0$
i.e., electric field inside a hollow sphere is zero.