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If F1 and F2 are the strengths of magnetic fields at same distance ‘d' , from the centre of a bar magnet, on axial and equatorial lines respectively, show that F1/F2 =2+7l^2/d^2 , where ‘l’ is the magnetic length.

If F1 and F2 are the strengths of magnetic fields at same distance ‘d' , from the centre of a bar magnet, on axial and equatorial lines respectively, show that F1/F2 =2+7l^2/d^2 , where ‘l’ is the magnetic length.

Grade:12

1 Answers

ROSHAN MUJEEB
askIITians Faculty 829 Points
one year ago

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=

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

=

μ
o




(d
1
2

−l
2
)
2

2Md
1




B
2

=

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

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