CBSE Class 12-science Answered
Q)Show that a planar loop carrying a current I, having N closely wound turns and area of cross section A, possesses a magnetic moment m=NIA.
Asked by Ibrahim Mohammed | 14 Feb, 2016, 05:35: PM
Expert Answer
Consider a plane loop of wire carrying current.
Looking at the upper face, current is anticlockwise. Therefore, it has a North polarity. Looking at the lower face of the loop, current is clockwise. Therefore, it has a South polarity. The current carrying loop thus behaves as a system of two equal and opposite magnetic poles and hence is a magnetic dipole.
The magnetic dipole moment of the current loop (M) is directly proportional to strength of the current (I) through the loop and the area enclosed by the loop.
i.e.,
where K is a constant of proportionality.
If we define unit magnetic dipole as that of a small one turn loop of unit area carrying unit current, then from eqn (1),
1 = K × 1 × 1 or K = 1
Therefore, from eqn (1), M = IA
For N such turns, M = NIA ... (2)
Note: Eqn (2) is valid for planar current loop of any shape and size.
Answered by Faiza Lambe | 15 Feb, 2016, 03:12: PM
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