Question

the radius of a circular plates of a parallel plate condenser is r. air is there dielectric the distance between plate if it's capacitance is equal to that of an isolated sphere of radius
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Answer 1

your complete question -> The radius of circular plates of a parallel plate condenser is r.Air is their as a dielectric.The distance between the plates if its capacitance is equal to that of an isolated sphere of radius r' is

solution : we know, capacitance of parallel plates capacitor , $C=\frac{\epsilon_0A}{d}$

where A is area of plate and d is the seperation between plates.

given, radius of plate is r

so, area of plate , A = πr²

so, capacitor of parallel plate capacitor, $C=\frac{\epsilon_0\pi r^2}{d}$

again, capacitance of spherical capacitor , $C=4\pi\epsilon_0R$, where R is the radius of spherical capacitor.

given, radius of spherical capacitor is r'

so, C = $4\pi\epsilon_0r'$

a/c to question,

capacitance of parallel plate = capacitance of sphere

or, $\frac{\epsilon_0\pi r^2}{d}=4\pi\epsilon_0r'$

so, d = r²/4r'

hence, seperation between parallel plate is r²/4r'

Answer 2

Answer:

r^2/4r'

Explanation:

Capacitance of parallel plates= Capacitance of isolated sphere

=>€°A/d = 4 π€° r'

=>€°(πr^2) /d= 4π€°r'

=>d= r^2/4r'