AP EAMCET Engineering 22 Apr 2019 Shift 1 Paper

The expression of the magnetic field normal to the plane of coil is,
Baxis=

µ0Nir2

2(r2+h2) 3 2

Baxis=

µ0Nir2

2r3(1+ h2 r2 ) 3 2

Baxis=

µ0Nir2

2r3

(1+

h2

r2

)

3

2

(using binomial expansion)
Baxis=

µ0Nir2

2r3

(1−

3

2

h2

r2

) .....(I)
The expression of the magnetic field at the centre of the coil is,
Bcentre=

µ0Ni

2r

......(II)
From equation (I) and (II)
Baxis=Bcentre(1−

3

2

h2

r2

)
Baxis=Bcentre−(

3

2

h2

r2

)Bcentre
Thus the magnetic field on axis is smaller than the field at thecentre by a fraction

3

2

h2

r2

.