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

The number of turns in the coil is 86.

Step-by-step explanation:

Given that,

The magnitude of maximum torque produced in the motor,
`\tau=1.7* 10^(-2)\ N-m`

Area of the coil,
`A=9* 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=(\tau)/(IAB)\\\\N=(1.7* 10^(-2))/(1.1* 9* 10^(-4)* 0.2)\\\\N=85.85\\\\N=86`

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