Question

Two concentric conducting spherical shells having radii a and b are charged to q₁& q₂ respectively. The potential difference between 1 & 2 will be

• A. $\frac{q_{1}}{4\pi\varepsilon_{0}a} - \frac{q_{2}}{4\pi\varepsilon_{0}b}$
• B. $\frac{q_{2}}{4\pi\varepsilon_{0}}\left( \frac{1}{a} - \frac{1}{b} \right)$
• C. $\frac{q_{1}}{4\pi\varepsilon_{0}}\left( \frac{1}{a} - \frac{1}{b} \right)$
• D. None of these.

Answer 1

Answer: (C)

$\frac{q_{1}}{4\pi\varepsilon_{0}}\left( \frac{1}{a} - \frac{1}{b} \right)$

Answer 2

The potential on the surface of the sphere 1 is given by

v₁ =$\frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}}{a} + \frac{1}{4\pi\varepsilon_{0}}\frac{q_{2}}{b}$ . . . . (1)

The potential on the surface of the sphere 2 is given by,

V₂ = $\frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}}{b} + \frac{1}{4\pi\varepsilon_{0}}\frac{q_{2}}{b}$

⇒ v = v₁ – v₂ ⇒ v = $\frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}}{a} - \frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}}{b}$

⇒ v= $\frac{q_{1}}{4\pi\varepsilon_{0}}\left( \frac{1}{a} - \frac{1}{b} \right)$