Problem 1 Figure 1 shows a closed loop of wire that consists of a pair of equal

Question

Problem 1 Figure 1 shows a closed loop of wire that consists of a pair of equal semicircles, of radius 3.7 cm, lying in mutually perpendicular planes. The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other. A uniform magnetic field B of magnitude 76 mT is directed perpendicular to the fold diameter and makes equal angles (of 45') with the planes of the semicircles. The magnetic field is reduced to zero at a uniform rate during a time interval of 4.5 ms. During this interval, what are the Magnetic field Adobe Conven or Exce Select R PHY Conver Micro Docum (a) magnitude and Engish (b) direction (clockwise or counterclockwise when viewed along the direction of B) of the emf induced in the loop? FIGURE 1 You ha

Explanation / Answer

Both half-circular surfaces are at an angle of 45 degrees to the filed. Hence the flux of a field B is

flux = B * pi R^2 * sin(45) = 1/2 (2) * pi * R^2 * B

This flux goes to zero in 4.5 ms.

Hence Faraday's law gives:

Emf = Delta(flux) / delta t
= 1/2 2* pi * (0.037m)^2 * 76*10^-3 T / (4.5* 10^(-3) s)
=51.3 mV

The direction of the current will be such as to counter clockwise the diminishing flux. You can figure that out.

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