A circular conducting loop of radius 21.0 cm is located in a region of homogeneo

Question

A circular conducting loop of radius 21.0 cm is located in a region of homogeneous magnetic field of magnitude 0.900 T pointing perpendicular to the plane of the loop. The loop is connected in series with a resistor of 199 . The magnetic field is now increased at a constant rate by a factor of 2.30 in 21.0s.
a. Calculate the magnitude of the induced emf in the loop while the magnetic field is increasing.

b. Calculate the magnitude of the current induced in the loop while the field is increasing.

Explanation / Answer

induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt

where A = area

N = no. of tunrs

dB/dt = rate of change of amgnetic flux

so here emf e = 1 * 3.14 * 0.21* 0.21 * (2.3-0.9)/21

emf e = 9.23 mV

-----------------------------------------------------

induced current i = e/R

where R = resisatnce

Current i = 9.23 e-3/199

i = 46.38 uA

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