## Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field acting perpendicularly to its

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?

in progress 0
1 year 2021-09-02T01:58:56+00:00 1 Answers 0 views 0

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.