Question

A circular conducting loop of radius 27.0 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 265 Ω. The magnetic field is now increased at a constant rate by a factor of 2.20 in 25.0s.
1. Calculate the magnitude of the induced emf in the loop while the magnetic field is increasing.

Remember the equation for the induced voltage, when everything is constant except the magnetic field.

Tries 0/20

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

3. With the magnetic field held constant at its new value of 1.98 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 9.70 s.

Answer 1

r= 0.27 m

B= 0.900 T

R= 265Ω

t= 25 s

The magnetic field is now increased at a constant rate by a factor of 2.20 so new B' =

B' = 2.20*0.900 = 1.98 T

flux  ϕ = B*A ( here A is area )

induced emf = change in flux = dϕ/dt   = d(B*A) /dt = A*dB/dt = A*ΔB/Δt = pi*r^2*ΔB/Δt = pi*r^2*(B'-B) /t

= pi*0.27^2* ( 1.98-0.900) /25 = 0.00989375 V = 9.89375 × 10^-3 answer

2 )

current induced =   induced emf /R =0.00989375 /265 = 3.73349057*10^-5 A answer

3)
B'= 1.98

t= 9.7 s

after loop s out of the field , field will be zero

average induced voltage = A*ΔB/Δt = pi*0.27^2 * ( 1.98- 0) / 9.7 = 4.67488419 × 10^-2 V answer

Good Luck !!
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