Question

A flat coil, in the shape of a spiral, has a large number of turns N. The turns are wound tightly and the
inner and outer radii of the coil are a and b respectively. A uniform external magnetic field (B) is
applied perpendicular to the plane of the coil. Find the emf induced in the coil when the field is made
dB
to change at a rate
dB/dt​

Answer 1

Answer:

Magnetic field due to a coil of radius r at its center =

2r

μ

o

I

The thickness of the wire(t)=

n

b−a

Let us choose a loop at radius x and thickness dx

The thickness through dx is I

T

dx

Using this in formula:

We get magnetic field due to dx is

2xt

μ

o

Idx

For total magnetic field we need to integrate from a to b and substitute value of t.

Net magnetic field =∫

a

b

2xt

μ

o

Idx

Magnetic Field =

2(b−a)

μ

o

nIlog

e

(

a

b

)