Question

A thick shell with inner radius $R$ and outer radius $3R$ has a uniform charge density $\sigma c/m^3$. It has a spherical cavity of radius $R$ as shown in the figure. the electric field at the centre of the cavity is

• A. zero
• B. $2\sigma R/{\epsilon }_0$
• C. $3\sigma R/4{\epsilon }_0$
• D. $7\sigma R/12{\epsilon }_0$

Answer 1

The correct option is A zero

The cavity has radius R and having zero volume,

So, net charge at center of the cavity is zero, $q=0$

Apply Gauss's law,

$E.A=\frac{q}{{\epsilon }_o}=0$

$\Rightarrow E=0$

Hence, electric field at center of the cavity is zero.