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A magnetic dipole is under the influence...

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is `60^(@)` and one of the fields has a magnitude of `1.2 xx 10^(-2)` T. If the dipole comes to stable equilibrium at an angle of `15^(@)` with this field, what is the magnitude of the other field?

A

`3(sqrt3-1)xx10^(-3)T`

B

`(sqrt3-1)xx10^(-3)T`

C

`6(sqrt3-1)xx10^(-3)T`

D

`2(sqrt3-1)xx10^(-3)T

Text Solution

Verified by Experts

The correct Answer is:
C

Here, `theta = 60^@, B_1 = 1.2 xx 10^(-2) T`
`theta_1 = 15^@ , theta_2 = 60^@ - 15^@= 45^@`
In equillibrium , torque due to two fields must balance `tau_1 = tau _2`
`MB_1 sin theta_1 = MB_2 sin theta_2`
`B_(2) = (B_1 sin theta_1)/(sin theta_2) = (1.2 xx 10^-2 sin 15^@)/(sin 45^@)`
`=(1.2 xx 10^-2 (sin 45^@ cos30^@- cos 45^@sin 30^@))/(sin 45^@)`
` =1.2 xx 10^(-2) [cos 30^@ - sin 30^@]`
`1.2 xx 10^(-2) ((sqrt(3))/(2)-1/2) = 6 (sqrt(3) - 1) xx 10^(-3) T`.
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