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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

The magnetic field at the centre of a circular current carrying loop of radius 12 cm is 6 × 10−6 T. What will be the magnetic moment of the loop? - Physics

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प्रश्न

The magnetic field at the centre of a circular current carrying loop of radius 12 cm is 6 × 10−6 T. What will be the magnetic moment of the loop?

संख्यात्मक
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उत्तर

Data: R = 12 cm = 12 × 10−2 m,  B = 6 × 10−6 T, `µ_0/(4π)` = 107 T·m/A

B = `(µ_0NI)/(2R)`

The magnetic moment of the coil,

M = NIA = NI (πR2)

= `(2BR)/µ_0(πR^2)`

= `(2BR^3)/((µ_0/(4π)) xx 4)`

= `(BR^3)/(2((µ_0)/(4π)))`

= `((6 xx 10^-6)(12 xx 10^-2)^3)/(2 xx 10^-7)`

= 30 × 1728 × 10−6

= 5.184 × 10−2 A.m2

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