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A uniform magnetic field B exists in a d...

A uniform magnetic field B exists in a direction perpendicular to the plane of a square frame made of copper wire. The wire has a diameter of 2 mm and a total length of 40cm. The magntic field changes with time at a steady rate `(dB)/dt = 0.02 T s ^(-1)`. Find the current induced in the frame. Resistivity of copper `=1.7 X 10 ^(-8) Wm`.

Text Solution

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The resistance of the wire
`R=(rho l)/(pir^(2))=((1.7xx10^(-8))xx(0.40))/(pi(10^(-3))^(2))`
`=2.16xx10^(-3)Omega`
The area of the loop `=0.10xx0.10=10^(-2)m^(2)`
The induced emf `|e|=A((dB)/(dt))`
`=10^(-2)xx(0.02)=2xx10(-4)V`
The induced curretn `i=e/R=(2xx10^(-4))/(2.16xx10^(-3))`
`=9.3xx10^(-2)A`
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