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Consider a current loop where the circulating current is I. This may be for an example of a coil carrying a current. We will assume that the current loop lies within a single plane. The area enclosed by the current by the current is A suppose that μn is a unit vector coming out from the area A. The direction of μn is such that looking along it, the current circulates clockwise. Then the magnetic dipole moment or simply the magnetic moment μm is defined as
μm = I A μn
Magnetic dipole moment measures the strength of the magnetic field created by a current loop and also the extent of interaction of the current loop with an extremely applied magnetic field. When a magnetic moment is positioned in a magnetic field, it experiences a force torque that tries to rotate magnetic current to align its axis with the magnetic field. Since a magnetic moment is a current loop, it gives rise to a magnetic field B around it. Which is similar to a magnetic field around the bar magnet. The field B at a point P at a distance r along the axis of the coil from the centre is directly propositional to the magnitude of the magnetic moment but inversely propositional to the r3 that is
B α μm/r3
how to solve kcl
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