Question

(a) Define the term ‘mutual inductance’. 

Deduce the expression for the mutual inductance of two long coaxial solenoids having different radii and different number of turns. 

(b) A coil is mechanically rotated with constant angular speed w in a uniform magnetic field which is perpendicular to the axis of rotation of the coil. The plane of the coil is initially held perpendicular to the field. Plot a graph showing variation of (i) magnetic flux ϕ and (ii) the induced emf in the coil as a function of ωi

Answer 1

(a) Mutual inductance of solenoid S₂ with respect to solenoid S₁, is defined as total magnetic flux linked with solenoid S₂ for unit current flow in solenoid S₁.

Figure shows two long coaxial solenoids, each of length l, number of turns per unit length n₁ and n₂ wound one over the other. If current I flows through the outer solenoid S₂, a uniform magnetic field is set up in both solenoids.

 

(b) The plane of the coil is in yz plane and perpendicular to the x-axis i.e., direction of magnetic field.

A maximum magnetic flux Φ_max = B| A|.
As the coil rotates with angular speed ω, magnetic flux at any instant t, (or at angle ωt)
Φ  =| B| |A|cosωt