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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 palne of a square frame made of copper wire. The wire has a total length of `40cm` . The magnetic field changes with time at a steady rate `(dB//dt)=0.02T//sec` . Find the current induced in the frame. Resistance of wire `=I0Omega`

Text Solution

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Total length of wire `=40cm` i.e. each side of square `=10cm`
Flux passing through frame
`phi=BA=Bl^(2)`
`e=(dphi)/(dt)l^(2)=0.02xx(0.1)^(2)=2xx10^(-4)V`
`I=(e)/(R)=(2xx10^(-4))/(10)=2xx10^(-5)A`
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Knowledge Check

  • A copper wire of length 40cm, diameter 2mm and resistivity 1.7xx10^(-8)Omega m forms a square frame. If a uniform magnetic field B exists in a direction perpendicular to the plane of square frame and it changes at a steady rate (dB)/(dt)=0.02 T/s, then find the current induced in the frame.

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    D
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  • A copper wire of length 40 cm, diameter 2mm and resistivity 1.7xx10^(-8)Omega m form a square frame. If a uniform magnetic field B exists in a direction perpendicular to the plane of square frame and it changes at a steadyrate (dB)/(dt)=0.02 T/s, then find the current induced in the frame.

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  • A uniform magnetic field B exists in a cylindrical region of radius I0cm as shown in figure. A uniform wire or length 80cm and resistance 44.0Omega is bent into a square frame and is placed with one side along a diameter of the cylindrical region. if the magnetic field increases at a constant rate of 0.0I0T//sec , the current induced in the frame

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