A small magnet placed at a distance of 20 cm on the arm of a deflection magnetometer set in tanA position produces a deflection of 60 degree. The magnet is cut in three equal parts if one part is placed at the same distance in tanA position then what will be the new deflection

Given that,
d
1
​
=18cm,
d
2
​
=36cm,
l
1
​
=l
2
​

m
2
​
=16m
1
​
,
we have,
For Tan A position
4π(d
1
​
)
3

2μ
0
​
M
1
​

​
=B
H
​
tanθ
1
​

and for Tan B position
4π(d
1
​
)
3

μ
0
​
M
2
​

​
=B
H
​
tanθ
2
​

⇒
M
2
​

2M
1
​

​
=
d
2
3
​
tanθ
2
​

d
1
3
​
tanθ
1
​

​

But, M = ml, hence,
16m
1
​

2m
1
​

​
=
d
2
3
​
tanθ
2
​

d
1
3
​
tanθ
1
​

​

tanθ
1
​

tanθ
2
​

​
=
d
2
3
​

8×d
1
3
​

​

tanθ
1
​

tanθ
2
​

​
=
(36)
3

8(18)
3

​

tanθ
1
​

tanθ
2
​

​
=1
tanθ
2
​
=tanθ
1
​

θ
2
​
=θ
1
​
=30
∘