A rectangular loop of sides of length l and b is placed in x-y plane. A uniform but time varying magnetic field of strength B→=20ti^+10t2j^+50k^ where t is time elapsed. The magnitude of induced e.m.f. at time t is

s→=(ab)k^→perpendicular to x-y planeϕ=B→⋅S→=(50)(ab)= constant dϕdt=0∴ e=o

A rectangular loop of sides of length l and b is placed in x-y plane. A uniform but time varying magnetic field of strength B→=20ti^+10t2j^+50k^ where t is time elapsed. The magnitude of induced e.m.f. at time t is

s→=(ab)k^→perpendicular to x-y planeϕ=B→⋅S→=(50)(ab)= constant dϕdt=0∴ e=o

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A rectangular loop of sides of length l and b is placed in x-y plane. A uniform but time varying magnetic field of strength $\vec{B} = 20 t \hat{i} + 10 t^{2} \hat{j} + 50 \hat{k}$ where t is time elapsed. The magnitude of induced e.m.f. at time t is

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zero

20t

20 + 20t

answer is D.

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Detailed Solution

$\vec{s} = (ab) \hat{k} \to$ perpendicular to x-y plane
$ϕ = \vec{B} \cdot \vec{S} = (50) (ab) = constant$
$\begin{array}{l} \frac{d ϕ}{dt} = 0 \\ ∴ e = o \end{array}$

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A rectangular loop of sides of length l and b is placed in x-y plane. A uniform but time varying magnetic field of strength B→=20ti^+10t2j^+50k^ where t is time elapsed. The magnitude of induced e.m.f. at time t is

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A rectangular loop of sides of length l and b is placed in x-y plane. A uniform but time varying magnetic field of strength $\vec{B} = 20 t \hat{i} + 10 t^{2} \hat{j} + 50 \hat{k}$ where t is time elapsed. The magnitude of induced e.m.f. at time t is