Question

A large, 60 turn circular coil of radius 10.0 cm carries a current of 4.2 A. At the center of the large coil is a small 20 turn coil of radius 0.5 cm carrying a current of 1.0 A. The planes of the two coils are perpendicular. Find the torque exerted by the large coil on the small coil. (Neglect any variation in B due to the large coil over the region occupied by the small coil.)

Answer 1

To solve this problem we apply the concepts related to the electric torque generated by the electromagnetic field. Mathematically this Torque can be written under the following relation

$\tau = NIAB sin\theta$

Here,

N = Number of Turns

I = Current

A = Area

B = Magnetic Field

The maximum torque will be reached when the angle is 90 degrees, then we will have the following relation,

$\theta = 90\°C$

Magnetic Field is given at function of the number of loops, permeability constant at free space at the perimeter, then

$B = \frac{N\mu_0 I}{2\pi r}$

$B = \frac{(60)(4\pi * 10^{-7})(4.2)}{2\pi (0.1)}$

$B = 5.04*10^{-4}T$

Replacing at the first equation we have,

$T = (20)(\pi (0.005)^2)(1)(5.04*10^{-4})$

$T = 7.91*10^{-7}N\cdot m$