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Question : 28
Total: 30
Draw a labelled diagram of Van de Graff generator. State its working principle to show how by introducing a small charged sphere into larger sphere, large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.
OR
(a) Deduce the expression for the torque acting on a dipole of dipole moment
(b) Consider two hollow concentric spheres,S 1 S 2 2 Q 4 Q
(i) Find out the ratio of the electric flux through them.
(ii) how will the electric flux through the sphereS 1 ε r ′ ε r S 1
Deduce the necessary expression.
OR
(a) Deduce the expression for the torque acting on a dipole of dipole moment
(b) Consider two hollow concentric spheres,
(i) Find out the ratio of the electric flux through them.
(ii) how will the electric flux through the sphere
Deduce the necessary expression.
Solution:
OR
(a) Consider an electric dipole consisting of charges→ q + q 2 a
θ
Force on charge− q A = − q
Force on charge+ q B = + q
(
)
Electric dipole is under the action of two equal and unlike parallel force, which give rise to a torque on the dipole.
τ = Force ×
τ = q E ( A N ) = q E ( 2 a s i n θ )
τ = p E s i n θ [ ∵ 2 q a = P ]
=
×
(b) (i) Charge enclosed by sphereS 1 = 2 Q
By Gauss' law, electric flux through sphereS 1
ϕ 1 =
Charge enclosed by sphereS 2
Q ′ = 2 Q + 4 Q = 6 Q
Electric flux through sphereS 2
∴ ϕ 2 =
The ratio of the electric flux is
=
=
=
(ii) For sphereS 1
∴ ϕ ′ =
⇒
=
⇒ ϕ ′ = ϕ 1 ×
∵ ε r > ε 0
∴ ϕ ′ < ϕ 1
(a) Consider an electric dipole consisting of charges
Force on charge
Force on charge
Electric dipole is under the action of two equal and unlike parallel force, which give rise to a torque on the dipole.
(b) (i) Charge enclosed by sphere
By Gauss' law, electric flux through sphere
Charge enclosed by sphere
Electric flux through sphere
The ratio of the electric flux is
(ii) For sphere
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