Question

A circular coil with a cross-sectional area of 4 cm² has
10 turns. It is placed at the centre of a long solenoid that
has 15 turns/cm and a cross-sectional area of 10 cm², as
shown in the figure. The axis of the coil coincides with the
axis of the solenoid. What is their mutual inductance?
(a) 7.54 uH
(b) 8.54 uH
(c) 9.54 HH
Ni turns
S2
(d) 10.54 uH
N2 turns​

Answer 1

Answer:

Given : Number of turns in coil N

2

=10

Number of turns per unit length in solenoid, n=15 per cm =1500 turns per meter

Area of the coil A

2

=4 cm

2

=4×10

−4

m

2

Mutual inductance M=μ

o

nN

2

A

2

cosθ, where θ is the angle between

B

and

A

2

∴ M=4π×10

−7

×1500×10×4×10

−4

×1 (∵θ=0

o

)

⟹M=7.54×10

−6

H=7.54μH