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Please give the derivation of Magnetic Field at

1: Axial Position

2: Equatorial Position

Your query is incomplete. 

Refer to the following links to find magnetic field at the axial line and equatorial line of a bar magnet.

Axial line:

https://www.meritnation.com/ask-answer/question/in-the-given-figure-two-points-p-and-q-are-located-at-dista/magnetism-and-matter/1751418

Equatorial line:

https://www.meritnation.com/ask-answer/question/how-can-we-prove-that-the-magnetic-field-at-a-point-on-the-e/magnetism-and-matter/1466659

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The above diagram depicts the magnetic field at axial position

2 At the equatorial line

Let P be a point on the equatorial line of a short bar magnet where flux densitydue to the magnet is to be found out.

 

magnetic dipole of equatorial line of a short bar magnet

 

SN = 2l,

Magnetic flux density at p due to N-pole is

Magnetic flux density at p due to s-pole is

B1 = B2

The resultant magnetic flux density at P is

Since the bar magnet is short d >> l, l2 can be neglected as compared to d2.

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