First slide

Electric field

Question

In the figure shown, find the ratio of the linear charge densities $λ_{1}$ (on semi-infinite straight wire) and $λ_{2}$ (on semi-circular part), that is $λ_{1} / λ_{2}$ so that the field at O is along y direction.

Difficult

A

2
B

1.5
C

3
D

2.5

Solution

Electric field due to semi-circular part: $E_{2} = \frac{λ_{2}}{2 {πε}_{0} R}$
Electric field due to straight part: $E_{1 x} = E_{1 y} = \frac{λ_{1}}{4 {πε}_{0} R}$
For net field to be along y-axis: $E_{2} = E_{1 x} \Rightarrow \frac{λ_{2}}{2 {πε}_{0} R} = \frac{λ_{1}}{4 {πε}_{0} R} \Rightarrow \frac{λ_{1}}{λ_{2}} = 2$

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