Explain the equivalence between a magnetic dipole and (a) current carrying circular coil (b) solenoid.
Answers
Answer :-
Magnetic dipole is an arrangement of two equal and opposite magnetic poles which are separated by a small distance.
Product of pole strength and magnetic length is, magnetic dipole moment of a magnetic dipole. It is vector directed from S-pole to N-pole.
Ampere stated that the distribution of force due magnetic lines around a finite current carrying solenoid is same to that produced by the bar magnet.
The magnetic induction at the point along the axis of a circular coil carrying current is (B) = μ₀nIa₂/ 2(a²+x²)³⁽²
For points which are far away from the coil, x very high than a, a2 is small and it is neglected. Hence for such points,
B = μ₀nIa₂/ 2(x³)
For circular loop, n = 1, its area A = πa²
B = μ₀IA/ 2Π(x³) - - - (1)
Magnetic induction along the axial line of a short bar magnet is
B = μ₀/4Π x 2M/x³
B = μ₀/2Π x M/x³ - - - (2)
Comparing (1) & (2)
M = I A - - -(3)
Magnetic moment of a current loop is termed as the product of current and the loop area. The direction is perpendicular to plane of loop.