Class 12 Physics
CBSE and UP Board
Magnetism and Matter
Chapter-5 Exercise 5.21
Additional Exercise
NCERT Solutions for Class 12 Physics Chapter 5 Question 21
A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60º, and one of the fields has a magnitude of 1.2 × 10⁻² T. If the dipole comes to stable equilibrium at an angle of 15º with this field, what is the magnitude of the other field?
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Magnitude of one of the magnetic fields, B₁ = 1.2 x 10-2 T
Magnitude of the other magnetic field = B₂
Angle between the two fields, 0 = 60°
At stable equilibrium, the angle between the dipole and field B₁, 0₁ = 15°
Angle between the dipole and field B2, 02 = 0 – 0₁ = 60° – 15° = 45°
At rotational equilibrium, the torques between both the fields must balance each other.
.-. Torque due to field B₁ = Torque due to field B2
MB₁ sin0₁ = MB2 sin02
Where,
M = Magnetic moment of the dipole
Therefore , B2 =( B₁ sin0₁ )/sin02
= 1.2 x10⁻2 x sin 15°/sin 45° = 4.39 x 10-3 T
Hence, the magnitude of the other magnetic field is 4.39 x 10-3 T.