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A spherical capacitor consists of two co...

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports. Show that the capacitance of this spherical capacitor is given by `C = (4pi in_(0) r_(1) r_(2))/(r_(1) - r_(2))`,
Where `r_(1) and r_(2)` are radial of outer and inner spheres respectively.

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To derive the capacitance of a spherical capacitor consisting of two concentric spherical conductors, we can follow these steps: ### Step 1: Understanding the System We have two concentric spherical conductors: an inner sphere with radius \( r_2 \) and an outer sphere with radius \( r_1 \). The inner sphere carries a charge \( -q \), and the outer sphere, which is grounded, will have an induced charge of \( +q \) on its inner surface and will remain neutral overall. ### Step 2: Define the Potential The potential \( V \) at a distance \( r \) from a point charge is given by the formula: \[ ...
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