A rectangular coil containing 20 loops (turns) 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 cm and $b= 12.0 \mathrm{~cm}$. The coil has a total resistance of $8.00 \Omega$.
(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 emf 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 emf is the same in both cases.

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I'll solve this problem step by step, carefully following the LaTeX formatting guidelines: : Calculate the Area of the Coil : Determine the Rate of Change of Magnetic Flux : Calculate Induced EMF for Different Situations : Explanation of Part (b) (a) See the detailed calculations in Step 3 (b) The induced EMF is the same because the rate of change of magnetic flux is constant during the linear motion of the coil.

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I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:

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: Calculate the Area of the Coil

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