Solveeit Logo
Login

Question

Question: A magnetic dipole is under the influence of two magnetic fields. The angle between the field directi...

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 x 10-2 T. If the dipole comes to stable equilibrium at an angle of 30° with this field, then the magnitude of the field is

A

1.2 x 10-4 T

B

2.4 x 10-2 T

C

1.2×10−2 T1.2 \times 10 ^ { - 2 } \mathrm {~T}

D

2.4×10−2 T2.4 \times 10 ^ { - 2 } \mathrm {~T}

Answer

1.2×10−2 T1.2 \times 10 ^ { - 2 } \mathrm {~T}

Explanation

Solution

: Here, , θ=60∘,B1=1.2×10−2 T\theta = 60 ^ { \circ } , B _ { 1 } = 1.2 \times 10 ^ { - 2 } \mathrm {~T}

θ2=60∘−30∘=30∘\theta _ { 2 } = 60 ^ { \circ } - 30 ^ { \circ } = 30 ^ { \circ }

in stable equilibrium, torques due to two fields must be balanced

i.e., τ1=τ2\tau _ { 1 } = \tau _ { 2 }

or B2=B1sin⁡θ1sin⁡θ2B _ { 2 } = B _ { 1 } \frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } }

=B2sin⁡30∘sin⁡30∘B1= B _ { 2 } \frac { \sin 30 ^ { \circ } } { \sin 30 ^ { \circ } } B _ { 1 }

=1.2×10−2 T= 1.2 \times 10 ^ { - 2 } \mathrm {~T}