A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I = I0 cos (300 t) where I0 is constant. If the magnetic moment of the loop is N µ0 I0 sin (300 t), then 'N' is

Engineering

Physics

Magnetic Flux and Faraday Law and Lenz Law

Solenoid and Toroid

Question

A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I = I₀ cos (300 t) where I₀ is constant. If the magnetic moment of the loop is N µ₀ I₀ sin (300 t), then 'N' is

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$B = \frac{μ_{0} I_{0} \cos 300 t}{10}$

$ϕ = \frac{μ_{0} I_{0}}{10} \times 3 .14 \times 0 .01 \cos 300 t$

$ϕ = 3 .14 \times μ_{0} I_{0} \cos 300 t \times 10^{- 3}$

$e = - \frac{dϕ}{dt} = 3 .14 \times 300 μ_{0} I_{0} \sin 300 t \times 10^{- 3}$

$i = \frac{e}{R} = \frac{3 .14 \times 300 μ_{0} I_{0} \sin 300 t \times 10^{- 3}}{0 .005}$

$i = 3 .14 \times 60 μ_{0} I_{0} \sin 300 t$

Magnetic moment