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Question

A time-dependent magnetic field B(t) is produced in a cylindrical region of radius R. The magnetic field is given as B(t)=B0t^z for 0r<R and zero for r > R, where B0 is a positive constant, ^r is the unit vector in the radially outward direction and ^θ is the unit vector in the tangential direction, such that ^r×^θ=^z. The electric field at r> R is

A
BoR2r^r
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B
BoR22r^θ
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C
BoR2r^r
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D
BoR22r^θ
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Solution

The correct option is C BoR22r^θ
Emf Generated = Rate of change of Flux ( sign due to the opposing nature of induced emf )
E.dl=d(BdA)dt
E(2πr)=B0πR2
E=B0R22r

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