Page 7 - English Class X_cbse new (FINAL).cdr

S. Solution Marking S. Solution Marking
Scheme No. Scheme
No.
[1]
3. E at point P is given by

cont. 2πa 4. Electrostatic field lines cannot form closed loops, because potential
always decreases in the direction of the field and its field energy is
E = ∫ dEcosθ consumed by the body to go from A and then back to A, while at the
0 same time its conservative character would ensure that this work
should be zero, which is a contradiction hence field lines not form
[∵ Only the axial components contribute towards electric field.] closed loops. [1]

=∫E2πa kq ⋅ dl ⋅ x
0 2πa r2 r

∫= kqx ⋅ 1 2πa 5. The tangent to a line of electric field at any point gives the direction
2πa r3 of the electric field at that point. If any two lines of electric field cross
dl each other, then at the intersection point, there would be two tangents
and hence two directions for
0 electric field, which is not possible. Hence, the electric field lines do
not cross each other.
∵ cosθ = x [1]
r 

kqx( )= ⋅ 1 2πa
2πa r3
0

( )= kqx ⋅ 1 3/2 ⋅ 2πa [1] 6. (i) The dipole moment of dipole is p = q × (2a)
2πa x2 + a2
Force on -q at A = −qE
r2 = x2 + a2 Force on +q at B = +qE
Net force on the dipole = qE − qE = 0
kqx
x2 + a2 3/2
( )E =
BE
qx
x2 + a2
( )= 1 ⋅ 3/2
4π ∈0
[1]
If x>>a, then x2 + a2 = x2 E [1]
[2]
( )E = 1 qx AN
4π ∈0 x2 3/2 5

E= 1 q (ii) Work done on dipole
4π ∈0 x2
[1] W = ∆U = pE(cosθ1 − cosθ2 )
This expression is similar to electric field due to point charge.
( )[3] = pE cos0 − cos180
W =2pE

7. Same as A6