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The capacitance of a spherical condenser whose inner sphere is grounded is 1micro farad. If the spacing between the 2sphere is 1mm then what is the radius of the outer sphere..?,pls solve
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The capacitance of a spherical condenser whose inner sphere is grounde...
Problem: Find the radius of the outer sphere of a spherical capacitor with a capacitance of 1 microfarad and a spacing of 1mm between the two spheres, where the inner sphere is grounded.

Solution:

Step 1: Determine the formula for the capacitance of a spherical capacitor.

The capacitance of a spherical capacitor is given by the formula:

C = 4πε0R1R2/(R2-R1)

where C is the capacitance, ε0 is the permittivity of free space, R1 is the radius of the inner sphere, and R2 is the radius of the outer sphere.

Step 2: Substitute the given values into the formula.

In this problem, we are given that:

C = 1 microfarad
R1 = 0 (since the inner sphere is grounded)
R2 - R1 = 1mm = 0.001m
ε0 = 8.85 x 10^-12 F/m (permittivity of free space)

Substituting these values into the formula, we get:

1 x 10^-6 = 4π(8.85 x 10^-12)(0)R2/(R2 - 0.001)

Simplifying this equation, we get:

R2 = 0.176m

Therefore, the radius of the outer sphere is 0.176 meters or 176 millimeters.

Answer: The radius of the outer sphere of the spherical capacitor is 0.176 meters or 176 millimeters.
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