Question

You have a wire of length L = 1.6 m for making a square coil of a dc motor. The current in the coil is I = 2.0 A, and the magnetic field of the motor has a magnitude of B = 0.34 T. Find the maximum torque exerted on the coil when the wire is used to make (a) a single-turn square coil and (b) a two-turn square coil.

Answer 1

a) Let's first find the side of the square:

$$a=\dfrac{L}{4}=\dfrac{1.6\ m}{4}=0.4\ m.$$

Then, we can find the maximum torque exerted on the coil when the wire is used to make a single-turn square coil from the formula:

$$\tau=NIAB sin\theta=NIa^2B sin\theta,$$ $$\tau=1\cdot2.0\ A\cdot(0.4\ m)^2\cdot0.34\ T\cdot sin90^{\circ}=0.1088\ N\cdot m.$$

b) We can find the maximum torque exerted on the coil when the wire is used to make a two-turn square coil from the same formula:

$$\tau=2\cdot2.0\ A\cdot(0.4\ m)^2\cdot0.34\ T\cdot sin90^{\circ}=0.2176\ N\cdot m.$$