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 emf at time t is:

Options

A. 20+20t
B. 20
C. 20t
D. zero

Explanation

To solve the problem, we need to find the induced electromotive force (emf) in a rectangular loop placed in a time-varying magnetic field. The magnetic field is given by:

\[ \vec{B} = 20t \hat{i} + 10t^2 \hat{j} + 50 \hat{k} \]

### Step 1: Determine the area vector of the rectangular loop
The rectangular loop lies in the x-y plane, which means its area vector \(\vec{A}\) will be perpendicular to the plane of the loop. For a loop with sides of length \(l\) and \(b\), the area vector can be expressed as:
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