Question

The field normal to the plane of a circular wire of N turns
and radius r which carries a current I is measured on the
axis of the coil at a small distance h from the centre of
the coil. This is smaller than the field at the centre by the
fraction

Answer 1

Answer:

Magnetic field at the centre B

c

=

2r

μ

0

ni

Magnetic field on the axis at a small distance h from the centre,

B

h

=

4π(r

2

+h

2

)

2

3

2nμ

0

i⋅πr

2

=

2(r

2

+h

2

)

2

3

nμ

0

i⋅r

2

=(

2r

nμ

0

i

)(1+

r

2

h

2

)

2

−3

≈(

2r

nμ

0

i

)(1+(

2

−3

)(

r

2

h

2

))

∴

B

c

B

c

−B

h

=

2r

2

3h

2

Explanation:

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