Question

Concentric metallic hollow spheres of radii $R$ and $4 R$ hold charges $Q _{1}$ and $Q _{2}$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V ( R )- V (4 R )$ is:

• A. $\frac{3 Q _{1}}{16 \pi \varepsilon_{0} R }$
• B. $\frac{ Q _{2}}{4 \pi \varepsilon_{0} R }$
• C. $\frac{3 Q _{1}}{4 \pi \varepsilon_{0} R }$
• D. $\frac{3 Q _{2}}{4 \pi \varepsilon_{0} R }$

Answer 1

Answer: (A)

$E=\frac{K Q_{1}}{r^{2}}$
$\Delta V=\int\limits_{R}^{4 R} E \, dr=\frac{3 K Q_{1}}{4R}$