Find the ratio of intensity of magnetic field at a point on axial and equatorial line. The
points are at equal distance from the centre of axis of a magnetic dipole
Answers
Answer:
We know that the magnetic field at a distance d from centre on the axis of a magnet of length 2l and magnetic moment M is given by:-
B=
4π
μ
o
(d
2
−l
2
)
2
2Md
For P
1
, d
1
=10cm
for P
2
, d
2
=d
1
+10=20cm
B
1
=
4π
μ
o
(d
1
2
−l
2
)
2
2Md
1
B
2
=
4π
μ
o
(d
2
2
−l
2
)
2
2Md
2
Given that :
B
2
B
1
=
2
25
⟹
d
2
d
1
(d
1
2
−l
2
)
2
(d
2
2
−l
2
)
2
=
2
25
⟹
20
10
(10
2
−l
2
)
2
(20
2
−l
2
)
2
=
2
25
⟹
(10
2
−l
2
)
2
(20
2
−l
2
)
2
=25
⟹
10
2
−l
2
20
2
−l
2
=5
⟹400−l
2
=500−5l
2
⟹4l
2
=100
⟹l
2
=25
⟹l=5cm
Hence,magnetic length = 2l=10cm