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29.57     The long, straight wire shown in Fig. P29.57a carries constant current I.  A metal bar with length L is moving at constant velocity v, as shown in the figure.  Point a is a distance d from the wire.

(a) Calculate the emf induced in the bar.

(b) Which point, a or b, is at higher potential?

(c) If the bar is replaced by a rectangular wire loop of resistance R (Fig. P29.57b), what is the magnitude of the current induced in the loop?

Hint: (b) and (c) are conceptual questions.

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Step 1

a)

As shown from the diagram, divide the total length of the rod into small number of elements dx which is at a distance x from current carrying wire.

Magnitude of magnetic field due to current carrying ire at a distance x from the element is

Step 2

The induced emf in a rod moves normal to magnetic field is

Step 3

b)

The magnitude of force acting on moving...

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