Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
Advertisement Remove all ads

The Current in a Long Solenoid of Radius R And Having N Turns per Unit Length is Given By I= I0 Sin ωT. a Coil Having N Turns is Wound Around It Near the Centre. - Physics


The current in a long solenoid of radius R and having n turns per unit length is given by i= i0 sin ωt. A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid ant the coil.

Advertisement Remove all ads



Radius of the long solenoid = R

Number of turns per unit length of the long solenoid = n

Current in the long solenoid, i =  i0 sin ωt

Number of turns in the small solenoid = N

Radius of the small solenoid = R

The magnetic field inside the long solenoid is given by

B = μ0ni

Flux produced in the small solenoid because of the long solenoid, ϕ = (μ0ni) × (NπR2)

(a) The emf developed in the small solenoid is given by

\[e =\frac{d\phi}{dt} = \frac{d}{dt}( \mu_0 niN\pi R^2 )\]

`e = μ_0nN πR^2(di)/(dt)`

Substituting i = i0 sin ωt, we get

e = μ0nNπR2i0ω cos ωt

(b) Let the mutual inductance of the coils be m.

Flux ϕ linked with the second coil is given by

ϕ = (μ0 ni) × (NπR2)

The flux can also be written as

ϕ = mi

∴ (μ0 ni) × (NπR2) = mi


m =  πμ0nNR2

Concept: Inductance - Mutual Inductance
  Is there an error in this question or solution?
Advertisement Remove all ads


HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 16 Electromagnetic Induction
Q 98 | Page 313
Advertisement Remove all ads
Advertisement Remove all ads

View all notifications

      Forgot password?
View in app×