First slide

Pseudo force

Question

Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density $σ$ . They are brought in contact and separated. What will be the new surface charge densities on them?

Moderate

A

$σ_{1} = \frac{5}{3} σ, σ_{2} = \frac{5}{6} σ$
B

$σ_{1} = \frac{5}{6} σ, σ_{2} = \frac{5}{2} σ$
C

$σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{6} σ$
D

$σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{3} σ$

Solution

$Q_{1} = σ 4 {πR}_{1}^{2} = σ 4 {πR}^{2} Q_{2} = σ 4 π (2 R)^{2} = σ 16 {πR}^{2} After Redistribution of charges \frac{Q_{1}^{'}}{Q_{2}^{'}} = \frac{R}{2 R} \Rightarrow Q_{2}^{'} = 2 Q_{1}^{'} . . (i) Q_{1}^{'} + Q_{2}^{'} = 20 {σπR}^{2} . . . (ii) From eq . (i) and (ii) \begin{array}{l} Q_{1}^{'} = \frac{20}{3} {σπR}^{2} \Rightarrow σ_{1}^{'} = \frac{5}{3} σ \\ Q_{2}^{'} = \frac{40}{3} {σπR}^{2} \Rightarrow σ_{2}^{'} = \frac{5}{6} σ \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App