What is magnetic dipole? obtain expression for the strength of magnetic field at a distance R from its centre on axial line
Answers
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 B
1
at P due to N pole of magnet ,
B
1
=
4π
μ
0
.
NP
2
m
or B
1
=
4π
μ
0
.
(r−l)
2
m
(along PX) .......................eq1
And , the magnetic field B
2
at P due to S pole of magnet ,
B
2
=
4π
μ
0
.
SP
2
m
or B
2
=
4π
μ
0
.
(r+l)
2
m
(along PS) ......................eq2
Therefore , resultant magnetic field at point P ,
B=B
1
−B
2
(-ive sign is due to opposite directionS of B
1
and B
2
)
It is clear from eq1 and eq2 that B
1
>B
2
,therefore the direction of B will be along PX .
or B=
4π
μ
0
.
(r−l)
2
m
−
4π
μ
0
.
(r+l)
2
m
(alongPX)
or B=
4π
μ
0
.
(r
2
−l
2
)
2
m(4rl)
(alongPX)
Now , m(2l)=M (magnetic dipole moment of magnet)
Hence , B=
4π
μ
0
.
(r
2
−l
2
)
2
2Mr
(alongPX)
solution