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A non conducting ring of radius R(1) is ...

A non conducting ring of radius `R_(1)` is charged such that the linear charge density is `lambda_(1)cos^(2)theta` where `theta` is the polar angle. If the radius is increased to `R_(2)` keeping the charge constant, the linear charge density is changed to `lambda_(2)cos^(2)theta`. The relation connecting `R_(1)`, `R_(2)lambda_(1)` and `lambda_(2)` will be

A

`lambda_(1)//R_(1)=lambda_(2)//R_(2)`

B

`lambda_(1)//R_(2)=lambda_(2)//R_(1)`

C

`lambda_(1)lambda_(2)=R_(1)R_(2)`

D

`lambda_(1)^(2)R_(1)=lambda_(2)^(2)R_(2)`

Text Solution

AI Generated Solution

To solve the problem, we need to derive a relation connecting the initial radius \( R_1 \), the new radius \( R_2 \), the initial linear charge density \( \lambda_1 \), and the new linear charge density \( \lambda_2 \). ### Step-by-Step Solution: 1. **Understanding the Charge Distribution**: - The linear charge density on the ring is given as \( \lambda_1 \cos^2 \theta \) for radius \( R_1 \). - When the radius changes to \( R_2 \), the linear charge density changes to \( \lambda_2 \cos^2 \theta \). ...
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