The long straight wire in the figure carries a current I that is decreasing with time at a constant rate.The circular loops A,B,and C all lie in a plane containing the wire.The induced emf in each of the loops A,B,and C is such that

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Quizplus · Accepted Answer

By Faraday's law, the induced emf in a closed loop is given by
$$\mathcal{E}=-\frac{d\Phi}{dt}$$
where $\Phi$ is the magnetic flux through the loop.
Let's consider each loop separately.
Loop A: The decreasing current in the wire will create a magnetic field that points into the page. As the field weakens, the flux through the loop will decrease, inducing a counterclockwise emf in the loop (Lenz's law). Therefore, the induced emf in loop A is counterclockwise.
Loop B: Since loop B is symmetric with respect to the wire, the flux through the loop due to the wire is zero (the flux lines always enter and exit the loop at opposite points, canceling each other out). Therefore, no emf is induced in loop B.
Loop C: Similar to loop A, the decreasing current will create a magnetic field that points into the page, inducing a counterclockwise emf in the loop.
Therefore, the induced emf in loop A is counterclockwise, the induced emf in loop B is zero, and the induced emf in loop C is clockwise. The only choice that matches this description is D.

The Long Straight Wire in the Figure Carries a Current