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A uniform but time-varying magnetic fiel...

A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region

A

is zero

B

Decreases as `1/r`

C

Increases as r

D

Decreases as `1/r^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
When he is running with rod in horizontal position, no field is cut by the rod, so e = 0 Construct a concentric circle of radius r. The induced electric field (E) at any point on the circle is equal to that at P . For this circle
`oint vecE.vecd| = |(dphi)/(dt)| = A|(dB)/(dt)|`
or `E xx (2pir) = pia^(2).|(dB)/(dt)|`
`rArr E = a^(2)/(2r) |(dB)/(dt)| rArr E prop 1/r`
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Knowledge Check

  • A uniform but time varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of paper as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region.

    A
    is zero
    B
    decreases as `(1)/(r )`
    C
    increases as r
    D
    decreases as `(1)/(r^(2))`

  • A uniform but time varying magnetic field B(t) exist in a circular region of radius a and is directed into the plane of the paper as shown. The magnitude of the induced electric field at point P at a distance r form the centre of the circular region.

    A
    is zero
    B
    decreases as `1/r`
    C
    increases as r
    D
    decreases as `1/r^2`

  • A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown in the figure. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region

    A
    is zero
    B
    decreases as `1/r`
    C
    increases as r
    D
    decreases as `1/r^2`

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