Here\'s an example to try on your own. On the next slide, we have four conductin

Question

Here's an example to try on your own. On the next slide, we have four conducting segments of wire (labeled 1,2,3.4) Segments 1 and 2 are placed together to form a fixed L shape. Segment 3 is horizontal and moving upward at a speed of 3 m/s. Segment 4 is vertical and moving to the right at a speed of 5 m/s. 3 is horizental and moving upward at a speed of 3 m/s Segment 4 is vertical ond moving to the right at a speed of 5 m/s At the moment shown, the four segments form a conducting square 50 cm on a side, with a resistance of 20 . A magnetic field is everywhere directed out of the screen with a magnitude of 2 T. Find the magnitude and direction (CW or CCW) of the current that is induced in the square at the moment depicted in the diagram. Answer: 0.4 A, CW

Explanation / Answer

Area of the square, A = xy

=> dA/dt = xvy + yvx

Induced current, I = (d/dt)/R = (B/R)(dA/dt) = B(xvy + yvx)/R = 2[(0.5 * 3) + (0.5 * 5)]/20 = 0.4 A

Since the area of the loop is increasing, magnetic flux is increasing. So, the induced current will be clockwise to oppose this increase in flux.

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