# Problem 4.

A rectangular coil containing 20 loops (barns) is moving with a constant speed of $5.00 \mathrm{~cm} / \mathrm{s}$ toward a region containing a uniform magnetic field of 3.00 T pointing into the page. The dimensions of the coil are $a=$ $8.00 \mathrm{~cm} \mathrm{and} b=12.0 \mathrm{~cm}$. The coil has a total resistance of 8.00 D .
(a) Consider four different situations: the coil is completely outside the field, half the coil has entered the field, the coil is entirely within the field, $75 \%$ of the coil has exited the field. In each of the four situations, determine the induced end and induced current in the coil. If the current is non-zero, use Lenz's law to determine if it is clockwise or counterclockwise.
(b) Compare the situation when half the coil has entered the field to the one when only $25 \%$ of it has entered the field. Explain why the induced end is the same in both cases.

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# Problem 4.

A rectangular coil containing 20 loops (barns) is moving with a constant speed of $5.00 \mathrm{~cm} / \mathrm{s}$ toward a region containing a uniform magnetic field of 3.00 T pointing into the page. The dimensions of the coil are $a=$ $8.00 \mathrm{~cm} \mathrm{and} b=12.0 \mathrm{~cm}$. The coil has a total resistance of 8.00 D .
(a) Consider four different situations: the coil is completely outside the field, half the coil has entered the field, the coil is entirely within the field, $75 \%$ of the coil has exited the field. In each of the four situations, determine the induced end and induced current in the coil. If the current is non-zero, use Lenz's law to determine if it is clockwise or counterclockwise.
(b) Compare the situation when half the coil has entered the field to the one when only $25 \%$ of it has entered the field. Explain why the induced end is the same in both cases.

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I'll solve this problem step by step, carefully following the LaTeX formatting guidelines: : Understand the Problem Setup : Calculate the Coil Area : Magnetic Flux Calculation : Induced EMF Calculation : Detailed EMF Calculations : Current Calculation (a) Induced EMF and current values: - Outside field: $\mathcal{E} = 0 \mathrm{~V}$, $I = 0 \mathrm{~A}$ - Half in field: $\mathcal{E} = -0.240 \mathrm{~V}$, $I = -0.0300 \mathrm{~A}$ (counterclockwise) - Entirely in field: $\mathcal{E} = 0 \mathrm{~V}$, $I = 0 \mathrm{~A}$ - 75% exiting: $\mathcal{E} = +0.240 \mathrm{~V}$, $I = +0.0300 \mathrm{~A}$ (clockwise) (b) The induced EMF is the same when half or 25% of the coil enters because the rate of change of magnetic flux is proportional to the velocity and the portion of the coil in the field.

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