A simple motor consists of a thin circular coil of wire with 250 turns and a rad

Question

A simple motor consists of a thin circular coil of wire with 250 turns and a radius of 1 cm. The mass of the coil is 50 g. A DC current of 2 A is applied to the wire, and the coil can rotate without friction in a constant field with magnitude B=0.04 T. The unit vector n is normal to the plane of the coil, and the angle between n and B is theta. The figure shows a view looking down the rotation axis of the coil, and I shows the direction of the current at the top of the coil.

The magnetic properties of electric currents are extremely important in many modern technologies, from electric motors to AC electric circuits and wireless cmmunication This assignment is designed to give you practice calculating magnetic forces, using the Biot-Savart Law to determine magnetic fields, and using the principle of superposition to compute the magnetic field produced by curren carrying wires in various configurations. (a) What is the magnetic moment of the coil, if the current is oriented as shown? Give a numerical answer for the magnitude and reference the direction to the coil, if the and/or Bas appropriate. (b) At what angles -is the magnitude of the magnetic torque on the coil the largest? Find all maxima for 0S0

Explanation / Answer

Given,

N = 250 ; r = 1 cm ; m = 50 g ; I = 2 A ; B = 0.04 T

a)We know tat the magnetic moment is given by:

(mu) = N I A

(mu) = 250 x 2 x 3.14 x 0.01^2 = 0.157 A m^2

Hence, mu = 0.157 A m^2

b)We know that the torque on a loop in magnetic field is given by:

tau = N B I A sin(theta)

sin(theta) has maximum value of 1 when theta = 90 deg

Hence, theta = 90 deg

tau = 250 x 0.04 x 2 x 3.14 x 0.01^2 x sin90 = 0.00628 N-m

Hence, tau = 0.00628 N-m

c)this might have two values,

tau = 0

tau = 0.00628 N-m

d)we know that,

tau = I alpha

aplha = tau/I

I = 0.05 x 0.01^2 = 0.000005 kg-m^2

alpha = 0.00628/0.000005 = 1256 rad/s^2

Hence, alpha = 1256 rad/s^2

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