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Question
The magnetic field at the centre of a circular loop of radius 12.3 cm is 6.4 x 10-6 T. What will be the magnetic moment of the loop?
Solution
Given:
B = 6.4 × 10-6 T,
R = 12.3 cm
= 12.3 × 10-2 m
To find: Magnetic moment (m)
Formula:
B = `(mu_0"IR"^2)/(2("z"^2 + "R"^2)^{3/2})`
Calculation:
From formula,
B = `(mu_0"I"pi"R"^2)/(2pi("z"^2 + "R"^2)^{3/2})`
= `(mu_0"m")/(2pi("z"^2 + "R"^2)^{3/2})` ....[∵ m = I(πR2)]
B = `(mu_0"m")/(2pi"R"^3)` .................(∵ z = 0)
∴ m = `("B" xx 2pi"R"^3)/mu_0`
= `(6.4 xx 10^-6 xx 2 xx pi xx (12.3 xx 10^-2)^3)/(4pi xx 10^-7)`
= `3.2 xx 10^{-6 + 7 - 6} xx (12.3)^3`
= {antilog (log 3.2 + 3 log 12.3)} × 10-5
= {antilog (0.5051 + 3.2697)} × 10-5
= {antilog (3.7748)} × 10-5
= 5.954 × 103 × 10-5
= 5.954 × 10-2 Am2
The magnetic moment of the loop is 5.954 × 10-2 Am2.
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