A wire forms a circular loop of radius R = 0.5 m in which a current of I = 10 A

Question

A wire forms a circular loop of radius R = 0.5 m in which a current of I = 10 A is maintained. The loop is positioned in the earth’s magnetic field with its plane parallel to the direction of the magnetic field. In this position the loop experiences a very small torque of 0.39×10-3 Nm. From the torque we can derive the magnitude of the earth’s magnetic field.

(a) Calculate the magnetic moment of the current carrying loop.
(b) Calculate the magnitude of the earth’s magnetic field.

The circular loop of wire from the above problem is now held with the plane perpendicular to the direction of the magnetic field? Which of the following will cause a current to be induced in the loop?

i) crushing the loop
ii) pulling the loop into a field-free region
iii) rotating the loop about an axis perpendicular to the field lines
iv) keeping the orientation of the loop fixed and moving it along the field lines

Explanation / Answer

Given that radius of the circular loop is R = 0.5m current in te wire is I = 10 A Loop experiences a torque = 0.39*10^-3 N -m a ) Magnetic moment of the current carrying loop is            = m * B magnetic field B = _0 i / 2R                           = 4*10^-7 *10 A / 2 * 0.5m                           = 4*10^-6 T                magnetic moment m = 0.39*10^-3 N -m / 4*10^-6 T                                                   = 97.5 m^2 A b )  magnetic field B = _0 i / 2R                           = 4*10^-7 *10 A / 2 * 0.5m                           = 4*10^-6 T                           = 4*10^-7 *10 A / 2 * 0.5m                           = 4*10^-6 T c ) The circular loop of wire from the above problem is now held with the plane perpendicular to the direction of the magnetic field i) crushing the loop
ii) pulling the loop into a field-free region
iii) rotating the loop about an axis perpendicular to the field lines
are correct

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