A rectangular coil of wire contains 110 loops and has dimensions a=0.400m and b=
ID: 2298153 • Letter: A
Question
A rectangular coil of wire contains 110 loops and has dimensions a=0.400m and b=0.300m. The coil is hinged to the y axis, and its plane makes an angle of 30 degrees with the x axis
a) For what orientation is the magnetic potential energy of the loop a minimum? What is the value of this energy?
b) When the loop is oriented so that it has its maximum magnetic potential energy, what are the net torque and net force acting on it
c) Why do electrons whose spins have the orientation discussed in the previous question rotate into the direction of the applied magnetic field?
Explanation / Answer
Potential energy U= -u.B where u is the magnetic moment equal to IA and B is the magnetic field.
1)Potential energy is minimum when the angle between Area and magnetic field is 90 deg. The direction of area is calculated by right hand screw rule where the fingers point is direction of current and thumb in the direction of area.So here value of potential energy is 0 since cos theta is 0.Direction of area is perpendicular to direction of plane of loop. So the loop will be parallel to the field.
2) For max potential energy , the angle theta between Area and field should be zero.Torque= niab sin theta=0, force=0 since each wire is experiencing a force of ILB sin theta.Opposites cancel
3)They do so to minimise the potential energy as every system wants to.When they are oriented in the direction of the field, energy is minimum.