© examsnet.com
Question : 24
Total: 26
SECTION - E
(a) Derive an expression for the electric field
(b) Draw a graph of
(c) If this dipole were kept in a uniform external electric field
OR
(a) Use Gauss's theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density
(b) An infinitely large thin plane sheet has a uniform surface charge density
Solution:
(a) Derivation of E
(b) Graph betweenE r
(c) (i) Diagrams for stable and unstable equilibrium of dipole
(ii) Torque on the dipole in the two cases
Electric field atP + q is E 1 =
Electric field atP − q E 2 =
Net electric Field atP
E 1 − E 2 =
−
=
( p = q .2 a )
Its direction is parallel to
(For short Dipole=
(i) For stable Equilibrium:
(ii) For unstable equilibrium:
Torque= 0
(Also accept,
=
×
∕ τ = p E s i n θ
OR
(a) Using Gauss's theorem to findE
(b) Expression for the work done to bring chargeq r
(a)
∮ E . d s =
The electric fieldE
Hence the net flux= ∮ E . d s =
=
= 2 E A
whereA
∴ ∮ E ⋅ d s =
=
= 2 E A
E =
(b)W = q
⋅
r
= q
( − E d r )
= − q
(
) d r
=
| ∞ − r |
= ( ∞ )
(b) Graph between
(c) (i) Diagrams for stable and unstable equilibrium of dipole
(ii) Torque on the dipole in the two cases
Electric field at
Electric field at
Net electric Field at
Its direction is parallel to
(For short Dipole
(i) For stable Equilibrium:
(ii) For unstable equilibrium:
Torque
(Also accept,
OR
(a) Using Gauss's theorem to find
(b) Expression for the work done to bring charge
(a)
The electric field
Hence the net flux
where
(b)
© examsnet.com
Go to Question: