Question

Suppose you wish to construct a motor that produces a maximum torque whose magnitude is 1.7 × 10-2 N·m. The coil of the motor has an area of 9.0 × 10-4 m2, consists of N turns, and contains a current of 1.1 A. The coil is placed in a uniform magnetic field of magnitude 0.20 T. What must N be?

Answer 1

Answer:

The number of turns in the coil is 86.

Explanation:

Given that,

The magnitude of maximum torque produced in the motor, $\tau=1.7\times 10^{-2}\ N-m$

Area of the coil, $A=9\times 10^{-4}\ m^2$

Current in the coil, I = 1.1 A

Magnetic field in the coil, B = 0.2 T

We need to find the value of N i.e. number of turns in the coil. The magnitude of torque attained in the coil is given by :

$\tau=NIAB\ sin\theta$

Here, $\theta=90^{\circ}$ (maximum)

$\tau=NIAB\\\\N=\dfrac{\tau}{IAB}\\\\N=\dfrac{1.7\times 10^{-2}}{1.1\times 9\times 10^{-4}\times 0.2}\\\\N=85.85\\\\N=86$

So, the number of turns in the coil is 86. Hence, this is the required solution.