A circular metal loop whose radius is 6:0 cm carries a current of 5:0 A. It is h

Question

A circular metal loop whose radius is 6:0 cm carries a current of 5:0 A. It is horizontal, while the
earth's field points North and 60? below the horizontal. (The earth's field has a magnitude of about
0:50 Gauss, which is 0:5 10?4 T.
a) If the current flows clockwise as viewed from above, then what is the magnitude and direction of
the magnetic moment vector?
b) What is the torque on the loop due to the earth's B-field?
c) The loop would have the least possible energy if its magnetic moment were parallel to the B-eld.
How much work is needed to move it from this parallel position to the horizontal position described
at the start?

Explanation / Answer

lets take upward to be (hat{j}) and north to be (hat{i}) and (hat{k}) in east. then (hat{A} = -hat{j}) (B_{earth} = 2.5 (hat{i} - sqrt{3} hat{j}) kT ) (a) (ec{mu} = I ec{A} = - 0.05654867 hat{j} Amp-m^2 ) i.e. towards down. (b) (ec{ au} = ec{mu} imes ec{B_{earth}} = - 141.37166941 hat{k} N-m^2 ) i.e. towards west. (c) change in potential energy, ( - Work done = Delta U = -Delta (ec{m} cdot ec{B}) = mB (cos heta - 1) ) if ( heta) is the angle between the m and B. here ( heta = 30^o ) (Work done = 37.880426 J )

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