JEE Mains 2020 Model Paper 4 New Pattern

Energy density in air gap, U0 =

1

2

ε0E02

Energy density in the dielectric
U =

1

2

ε0KE2 =

1

2

ε0K(

E0

K

)2 =

1

K

.

1

2

ε0E02 =

1

K

U0
Now, U = stored energy = U ´volume
∴ U0 = energy stored in air gap = U0 × volume of air gap = U0 × A (d - t)
=

1

2

ε0E02A(d−t)
Similarly energy stored in dielectric
UD = U × volume of dielectric slab =

1

K

1

2

ε0E02×A×t .
Hence, ratio

UD

Utotal

=

UD

UDU0

=

t

(s−t)K+t

Now, if

UD

Utotal

= 0.5 , then

t

(d−t)K+t

= 0.5 s
As K = 3 , so , t =

3d

4