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.)

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

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,

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

Replacing at the first equation we have,

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