Question

Equivalent magnetic moment calculation formula

Answer 1

Magnetic Moment Formula: Calculation for a Bar Magnet

(a) If a magnet of length l and magnetic moment M gets bent in the form of a semicircular, then its new magnetic see moment will be M’ = 2M/π



(b) The magnetic moment of a given electron because of its orbital motion is 1μB. But due to its spin motion, it will be μB /2.

i.e. Morbital = 

and Mspin = s 

Here μB = Bohr magneton

(i) The value of Bohr magneton μB = eh / 4πm

(ii) μB = 0.93 × 10–23 Amp-m2

(c) Other formulae for magnetic moments:

(i) M = ni r2

(ii) M = eVr/2 = er2ω/2 = er22πf/2 = er2π/T

(iii) e/mJ

(iv) M = nωB

(d) How can we calculate resultant magnetic moment? 

(i) When two bar magnets are lying mutually perpendicular to each other, then

M = √M12 + M22 = √2mpl

When two coils with a radius of r and carrying current I each, are lying concentrically with their planes at right angles to each other, then

M = √M12 + M22 = √2iπr2 if M1 = M2



Illustration: A square loop OABCO of side l carries a current i. Now, find the magnetic moment of the loop.

Solution: Magnetic moment of the loop can be written as,

M = i (BC x CO), where the letters in bold denote the vectors

BC = -lk



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