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 $2 \, m$ ?

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

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
$\int_{ s } \vec{ E } \cdot \vec{ d } s =\frac{1}{\varepsilon_0} \times$ charge enclosed or $E \times 4 \pi r ^2=\frac{1}{\varepsilon_0} \times 0 \Rightarrow E =0$
i.e., electric field inside a hollow sphere is zero.