Question

The electric field at point P just outside the outer surface of a hollow spherical conductor of inner radius 10 cm and outer radius 20 cm has magnitude 450 N/C and is directed outward. When an unknown point charge Q is placed at the center of the sphere, the electric field at point P is still pointing outward but is now 180 N/C. What is the value of charge Q?

• A. 4.5 nC
• B. 1.5 nC
• C. -1.5 nC
• D. –1.2 nC

Answer 1

The correct option is D –1.2 nC

$q_{net}=\frac{E{r}^2}{k}=\frac{450\times 0.04}{9\times {10}^9}=+20nC$

$q_{tot}=\frac{E{r}^2}{k}=+\frac{180\times 0.04}{9\times {10}^9}=+0.8nC{q}_{tot}=q_{net}+QQ=q_{tot}-q_{net}=+0.8-2.0=-1.2nC$