Question

A long solenoid has n turns per unit length and carries a current i =i, sin ot. A coil of N turns and area
A is mounted inside the solenoid and is free to rotate about its diameter that is perpendicular to the axis
of the solenoid. The coil rotates with angular speed o and the time 1 = 0 the axis of the coil coincides
with the axis of the solenoid as shown in figure. Write emf induced in the coil as function of time.
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Answer 1

Explanation:

The current flowing through the solenoid is I=I

o

sinwt

∴ Magnetic field due to solenoid B=μ

o

nI=μ

o

nI

o

sinwt

Flux through the solenoid ϕ=B×πa

2

=μ

o

nI

o

(πa

2

)sinwt

∴ Emf induced ∣E∣=

dt

dϕ

=μ

o

nI

o

w(πa

2

)coswt .............(1)

As B increases with time, thus induced current (i) flows in clockwise direction to prevent the increase in flux (Lenz Law).

Given : Resistivity of the cylindrical vessel is ρ

Cross-sectional area through which the induced current flows A=Ld

Thus resistance of the cylindrical vessel r=ρ

Ld

2πR

∴ Induced current i=

r

E

=

ρ(2πR)

μ

o

nI

o

w(πa

2

)Ld

coswt