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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
`oint (vec E).(vec dl)=(d phi)/(dt)((vec B)(vec A))=(d)/(dt) (BA cos(0^@))=A(dB)/(dt)`
`implies E(2 pi r)=(pi)(a^2)(dB)/(dt) for rgea`
`implies E=(a^2)/(2r)(dB)/(dt)implies 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.

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    is zero
    B
    decreases as `1/r`
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  • 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

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    is zero
    B
    decreases as `1/r`
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