Question

Two copper spheres having same radii, one solid and other hollow, are charged to the same potential. Which of the following statements is correct?

• A. Hollow sphere will hold more charge
• B. Solid sphere will hold more charge
• C. Solid sphere will have uniform volume charge density
• D. Both spheres will hold same charge

Answer 1

The Correct Option is D

Capacitance of the solid sphere $=4 \pi \varepsilon_{0} R$ where, $R$ is radius of the sphere.
Capacitance of the hollow sphere
$=4 \pi \varepsilon_{0} R$
Charge on the solid sphere $=\left(C_{\text {solid }}\right)$
$V=\left(4 \pi \varepsilon_{0} R\right)(V)$
Charge on the hollow sphere
$=\left(C_{\text {hollow }}\right)(V)$
$=\left(4 \pi \varepsilon_{0} R\right)(V)$
$\Rightarrow C_{\text {solid }}=C_{\text {hollow }}$
Thus, both spheres will hold same charge.