Question #206917

The plane of a square wire circuit with side 4.0 cm long is at an angle of 45° with respect to a uniform magnetic field of 0.25 T. The wires have a resistance per unit length of 0.2. If the field drops to zero in 2.5 s, what magnitude current is induced in the square circuit?


1
Expert's answer
2021-06-15T08:38:54-0400

Gives

Length (l)=4.0cm

Angle(θ)\theta) =45°

Magnetic field (B)=0.25T

Rl=0.2\frac{R}{l}=0.2

Time=3.5sec

Magnetic flux

ϕ=B.Acosθ=0.25×16×104×cos45°=22×104Wb\phi=B.Acos\theta=0.25\times16\times10^{-4}\times cos45°=2\sqrt2\times10^{-4}Wb

e=dϕdte=\frac{d\phi}{dt}


e=BAcosθdt=22×1042.5=1.131×104Wb/sece=\frac{BAcos\theta}{dt}=\frac{2\sqrt2\times10^{-4}}{2.5}=1.131\times10^{-4}Wb/sec

Current


I=er=1.131×1040.2×4×102=22.62×106AI=\frac{e}{r}=\frac{1.131\times10^{-4}}{0.2}\times4\times10^{-2}=22.62\times10^{-6}A

I=22.62μAI=22.62\mu A


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