Concentric metallic hollow spheres of radii

Question:

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

  1. $\frac{3 Q_{1}}{16 \pi \varepsilon_{0} R}$

  2. $\frac{Q_{2}}{4 \pi \varepsilon_{0} R}$

  3. $\frac{3 Q_{1}}{4 \pi \varepsilon_{0} R}$

  4. $\frac{3 Q_{2}}{4 \pi \varepsilon_{0} R}$


Correct Option: 1,

Solution:

$\mathrm{E}=\frac{\mathrm{KQ}_{1}}{\mathrm{r}^{2}}$

$\Delta V=\int_{R}^{4 R} E d r=\frac{3 K Q_{1}}{4 R}$

Leave a comment