Question

the inner and outer radii of a spherical capacitor are 50cm and 60cm respectively and a dielectric of constant 6 is filled in it . it's capacity will be
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Answer 1

Answer:

Given, a=50cm=0.5m

b= 60cm=0.6m

k= 6

Since, Capacitance of spherical capacitor=

4πε0k ab

(b-a)

So, C = 9×10^-9 × 6×0.5×0.6

(0.6-0.5)

= 0.3×9×6×10^-9

0.1

=3×54×10^-9

Capacitance, = 1.62×10^-7 farad

Answer 2

Answer:

Capacitance of spherical capacitor is 2 x 10⁻⁹F.

Explanation:

• The capacitance of a spherical capacitor whose inner radius is r2 and outer radius is r1, is given by:

$C = \frac{4\piε₀k(r1)(r2)}{(r1 - r2)}$

Given that :

• radius of inner sphere,r2 = 50 cm = 0.5 m
• radius of outer sphere, r1= 60 cm = 0.6 m
• dielectric constant = 6

Solution:

• The capacitance of the spherical capacitor is

$C = \frac{4\piε₀k(0.6)(0.5)}{(0.6 - 0.5)} \\ = \frac{1}{9 \times {10}^{9}} \times 6 \times \frac{0.3}{0.1} \\ = \frac{1}{9 \times {10}^{9}} \times 18 \\ C = 2 \times {10}^{ - 9} F$

• Hence, capacitance of spherical capacitor is 2 x 10⁻⁹F.