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 5.6 cm and rotates in a 0.24-T field. Coil 2 rotates in a 0.44-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2?

Answer 1

Answer:

4.14 cm.

Explanation:

Given,

For Coil 1

radius of coil, r₁ = 5.6 cm

Magnetic field, B₁ = 0.24 T

For Coil 2

radius of coil, r₂ = ?

Magnetic field, B₂ = 0.44 T

Using formula of maximum torque

$\tau_{max}= NIAB$

Since both the coil experience same maximum torques

now,

$NIA_1B_1 = NIA_2B_2$

$A_1B_1 = A_2B_2$

$r_1^2 B_1 = r_2^2 B_2$

$5.6^2\times 0.24= r_2^2\times 0.44$

$r_2 = 4.14\ cm$

Radius of the coil 2 is equal to 4.14 cm.