Question

derive an expression for the magnetic field due to a bar magnet at ​

Answer 1

Answer:

it's nothing like expressinon

Explanation:

there are some properties regards that

Answer 2

Answer:

Let NS be a bar magnet of magnetic length 2l and having each pole of magnetic strength m . O is the center of magnet and P is a point on axial line at a distance r from the center O of magnet , at which magnetic field has to be measured .

The magnetic field B1​ at P due to N pole of magnet ,

     B1​=4πμ0​​.NP2m​

or   B1​=4πμ0​​.(r−l)2m​   (along PX) .

And , the magnetic field B2​ at P due to S pole of magnet ,

     B2​=4πμ0​​.SP2m​

or   B2​=4πμ0​​.(r+l)2m​   (along PS) .

Therefore , resultant magnetic field at point P ,

      B=B1​−B2​  (-ive sign is due to opposite directionS of B1​ and B2​)

It is clear from eq1 and eq2 that B1​>B2​ ,therefore the direction of  B will be along PX .

or    B=4πμ0​​.(r−l)2m​−4πμ0​​.(r+l)2m​     (alongPX)

or    B=4πμ0​​.(r2−l2)2m(4rl)​     (alongPX)

Now , m(2l)=M (magnetic dipole moment of magnet)

Hence , B=4πμ0​​.(r2−l2)22Mr​     (alongPX)

Explanation: