A square conducting loop of side length and total resistance lies in a plane…

PHYSICS · Multi-part · CBSE · Physics · Electromagnetic Induction · Electromagnetic Induction

Problem

A square conducting loop of side length

a

and total resistance

R

lies in a plane perpendicular to a spatially uniform magnetic field. The magnitude of the field changes with time as described below: • From

t=0

t=t_{1}

the field increases linearly from

0

B_{\text{max}}

. • From

t=t_{1}

t=t_{2}

the field remains constant at

B_{\text{max}}

. • From

t=t_{2}

t=t_{3}

the field decreases linearly back to zero, with

t_{3}-t_{2}=t_{1}

. The field is directed out of the page throughout the entire process. (a) Sketch qualitatively the induced current

I(t)

versus time for the entire interval

0\le t\le t_{3}

, indicating the direction (clockwise or counter-clockwise) in each segment. (b) On the same time axis, sketch qualitatively the electrical power

P(t)

dissipated in the loop. Explain how the shape of the

P(t)

graph relates to that of

I(t)

. (c) Is the total electrical energy converted to thermal energy over the full cycle zero, positive, or negative? Justify your answer without performing detailed calculations.

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