A circular conducting loop of radius 15.0 cm is located in a region of homogeneo

Question

A circular conducting loop of radius 15.0 cm is located in a region of homogeneous magnetic field of magnitude 0.500 T pointing perpendicular to the plane of the loop. The loop is connected in series with a resistor of 147 Ohm. The magnetic field is now increased at a constant rate by a factor of 2.30 in 29.0s. Calculate the magnitude of the induced emf in the loop while the magnetic field is increasing. Calculate the magnitude of the current induced in the loop while the field is increasing. Ohm's law, again. With the magnetic field held constant at its new value of 1.15 T, calculate the magnitude of the average induced voltage in the loop while it is pulled horizontally out of the magnetic field region during a time interval of 4.90 s.

Explanation / Answer

The area of the loop is:

A = r^2 = * (0.15 m)^2 = 0.071 m^2

The change in magnetic flux is:

= AB = 0.071 m^2 * ((2.3 * 0.500 T) - 0.500 T) = 0.04615 Wb

The induced emf is:

= / t = 0.04615 Wb / 29 s = 1.59 x 10^-3 V

The induced current is:

I = / R = (1.59 x 10^-3V) / 147 = 10.75 µA = 10.75 x 10^-6 A

The change in magnetic flux is:

= AB = 0.071 m^2 * (0 T - 1.15 T) = - 0.08165 Wb

The average induced emf:

= - / t = 0.08165 Wb / 4.9 s = 0.01667 V

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