A rectangular loop of wire with sides H = 20 cm and W = 61 cm is located in a re

Question

A rectangular loop of wire with sides H = 20 cm and W = 61 cm is located in a region containing a constant magnetic field B = 0.55 T that is aligned with the positive y-axis as shown. The loop carries current i = 245 mA. The plane of the loop is inclined at an angle theta = 34 degree with respect t o t he x-axis. W hat is mu_x, the x-component of the magnetic dipole moment vector of the loop? What is mu_y the y-component of the magnetic dipole moment vector of the loop? What is T_z the z-component of the torque exerted on the loop? What are the x- and y- components the force F^rightarrow _bc exerted on segment bc of the loop? If the loop is released from its position, would it rotate? If so, in which direction (clockwise or counterclockwise)?

Explanation / Answer

Here ,

a) magnetic moment of loop , u = I * W * H

u = 245 *10^-3 * 0.20 * 0.61

u = 0.02989 A.m^2

the x component of magnetic dipole = - u * sin(theta)

x component of magnetic dipole = - 0.02989 * sin(34 degree)

x component of magnetic dipole = -0.0167 A.m^2

b)

y component of magnetic dipole = u * cos(theta)

y component of magnetic dipole = 0.02989 * cos(34 degree)

y component of magnetic dipole = 0.0248 A.m^2

c)

for the z component of the torque

z component of the torque = ux X By

z component of the torque = (-0.0167 i ) X ( 0.55 j )
  
z component of the torque = - 9.185 *10^-3 k N.m

the z component of the torque is - 9.185 *10^-3 N.m

d)

on the side bc

y component of the force = 0 N

x component of force = 0.55 * 0.20 * 0.245

x component of force = 0.02695 N

e)

it will rotate counterclockwise

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