Question

A circular conducting loop of radius 25.0 cm is located in a region of homogeneous magnetic field of magnitude 0.300 T pointing perpendicular to the plane of the loop. The loop is connected in series with a resistor of 283 Ω. The magnetic field is now increased at a constant rate by a factor of 2.80 in 19.0s.
Calculate the magnitude of the induced emf in the loop while the magnetic field is increasing.

Tries 0/20

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

Tries 0/20

With the magnetic field held constant at its new value of 0.84 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 8.30 s

Answer 1

here,

radis of loop , r = 25 cm

r = 0.25 m

magnetic feild , B = 0.3 T

resistance , R = 283 ohm

change in magnetic feild by a factor , B' = 2.8

time interval , t = 19 s

the magnitude of the induced emf in the loop, EMF = change in flux/time interval

EMF = B(2.8 - 1) * pi * r^2 / 19

EMF = 5.58 * 10^-3 V

the magnitude of the induced emf in the loop is 5.58 * 10^-3 V

the magnitude of the current induced in the loop , I = V/R

I = 5.58 * 10^-3 / 283

I = 1.97 * 10 ^-5 A

the magnitude of the current induced in the loop while the field is increasing is 1.97 * 10 ^-5 A

when magnetic feild is held constant

time interval , t' = 8.3 s

the magnitude of the average induced voltage in the loop , V' = change in flux/time interval

V' = (0.84 * pi * r^2* sin(90) - 0.83 * pi * r^2 * sin(0))/t'

V' = 0.84 * pi * 0.25^2 * 1 / 8.3

V' = 1.99*10^-2 V

the magnitude of the average induced voltage in the loop is 1.99*10^-2 V