A coil of wire containing N turns is in an external magnetic field that is perpendicular to the plane of the coil and it steadily changing. Under these circumstances, an emf ε is induced in the coil. If the rate of change of the magnetic field and the number of turns in the coil are now doubled (but nothing else changes), what will be the induced emf in the coil?

A coil of wire containing having N turns in an External magnetic Field that is perpendicular to the plane of the coil which is steadily changing. An Emf (∈) is induced in the coil.

To find :-

find the induced Emf if rate of change of the magnetic field and the number of turns in the coil are Doubled (but nothing else changes).

So,

Emf induced in the coil represented by formula

∈ = [tex]-N\frac{d\phi}{dt}[/tex] ...................(1)

Where:

. [tex]\phi = BAcos\theta[/tex] { B is magnetic field }

{A is cross-sectional area}

. [tex]N =[/tex] No. of turns in coil.

. [tex]\frac{d\phi}{dt} =[/tex] Rate change of induced Emf.

Here,

Considering the case :-

[tex]N1 = 2N[/tex] & [tex]\frac{d\phi1}{dt} = 2\frac{d\phi}{dt}[/tex]

Putting these value in the equation (1) and finding the new emf induced (∈1)

∈1 =[tex]-N1\times\frac{d\phi1}{dt}[/tex]

∈1 =[tex]-2N\times2\frac{d\phi}{dt}[/tex]

∈1 =[tex]4 [-N\times\frac{d\phi}{dt}][/tex]

∈1 = 4∈ ...............{from Equation (1)}

Hence,

The Resultant Induced Emf in coil is 4∈.