Question

Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field acting perpendicularly to its axis of rotation. Coil 1 has a radius of 4.0 cm and rotates in a 0.21-T field. Coil 2 rotates in a 0.45-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2

Answer 1

Answer:

The radius of coil 2 = 2.7 cm

Explanation:

The number of coils = 2

It is given that both carry equal current and rotates in the magnetic field.

The given radius of coil 1 = 4.0 cm

Coil 1 rotates = 0.21 T field

Coil 2 rotates = 0.45 T filed.

The radius of coil 2 need to be calculated.

Torque action on dipole is given by$T =NIABsinθ$

here T1 = T2

$r1^{2} \times B1 = r2^{2} \times B2 \\r2^{2} = 0.04 \times 0.04 \times \frac{0.21}{0.45} \\r2 = 0.027m \ or \ 2.7 cm$