Question

4. What distance d between the two parallel plates, each
of area A =
0.0314 m², of an air capacitor be kept so
that its capacitance is same as of a conducting sphere
of radius a = 0.5 m?​

Answer 1

We have to find the distance between two parallel plates , each of area A = 0.314 m², of an air capacitor be kept so that its capacitance is same as of a conducting sphere of radius 0.5 m.

solution : capacitance of sphere is given by, C = 4πε₀R

and capacitance of parallel plate capacitor is given by, C = ε₀A/d

a/c to question,

capacitance of parallel plate capacitor = capacitance of spherical capacitor

⇒ε₀A/d = 4πε₀R

⇒A/d = 4πR

here, A = 0.314 m², R = 0.5

so, 0.314/d = 4 × 3.14 × 0.5

⇒1/d = 4 × 10 × 0.5 = 20

⇒d = 1/20 m = 5 cm

Therefore the separation between the plates is 5cm.

Answer 2

Answer:

5mm

Explanation:

d=?

a=0.5m

A=0.0314 m sq

SOLN:

C=EA/d

C=4 pie E a

EA/d=4 pie E a

A=4 pie a d

A/4 pie a=d

d=0.0314/4x3.14x0.5

d=0.314/6.28

d=0.05

d=5mm