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A spherical capacitor consists of two co...

A spherical capacitor consists of two concentric spherical conductors , the inner one of radius `R_(1)` maintained at potential `V_(1)` and the outer conductor of radius `R_(2)` at potential `V_(2)` . The potential at a point P at a distance x from the centre (where `R_(2)gtxgtR_(1))` is

A

`((V_(1)-V_(2))(x-R_(1)))/((R_(2)-R_(1)))`

B

`V_(1)+(V_(2)x)/((R_(2)-R_(1)))`

C

`(V_(1)R_(1)(R_(2)-x)+V_(2)R_(2)(x-R_(1)))/((R_(2)-R_(1))x)`

D

`((V_(1)+V_(2)))/((R_(1)+R_(2)))x`

Text Solution

AI Generated Solution

The correct Answer is:
To find the potential at a point P located at a distance \( x \) from the center of a spherical capacitor consisting of two concentric spherical conductors, we can follow these steps: ### Step 1: Understand the Configuration We have two concentric spherical conductors: - Inner conductor with radius \( R_1 \) at potential \( V_1 \). - Outer conductor with radius \( R_2 \) at potential \( V_2 \). The point P is located at a distance \( x \) such that \( R_1 < x < R_2 \).
To find the potential at a point P located at a distance \( x \) from the center of a spherical capacitor consisting of two concentric spherical conductors, we can follow these steps: ### Step 1: Understand the Configuration We have two concentric spherical conductors: - Inner conductor with radius \( R_1 \) at potential \( V_1 \). - Outer conductor with radius \( R_2 \) at potential \( V_2 \). The point P is located at a distance \( x \) such that \( R_1 < x < R_2 \).
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