Question

a capacitor is filled with an insulator and a certain potential difference is applied to its plates. the energy stored in the capacitor is u. now the capacitor is disconnected from the source and the insulator is pulled out of the capacitor. the work done against the forces of electric field in pulling out the insulator is 4u. then dielectric constant of the insulator is

Please answer the question with explanation.
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Answer 1

Answer:

5

Explanation:

Let the initial capacitance be C

1

=

d

kε

0

A

⇒V

1

=

2

1

C

1

V

1

2

Let initial charge be Q and voltage be V

1

Now when the battery is removed Q becomes constant. When the insulation is removed c, decreases by k ∴ V increases by k.

C

2

=

d

ε

0

A

V

2

=V

1

k.

Now V=

2

1

C

1

v

1

2

final μ

2

=

2

1

k

C−1

(V

1

k)

2

=kμ

given work done =4μ

⇒4μ=kμ−μ

⇒k=5