A 200-loop coil of cross sectional area 8.5 cm2 lies in the plane of the page. An external magnetic field of
0.060 T is directed out of the plane of the page. The external field decreases to 0.020 T in 12 milliseconds.
(a) What is the magnitude of the change in the external magnetic flux enclosed by the coil?
(b) What is the magnitude of the average voltage induced in the coil as the external flux is changing? (c) If the coil has a resistance of 4.0 ohms, what is the magnitude of the average current in the coil?
To answer these questions, we need to use Faraday's Law of electromagnetic induction.
(a) The change in the external magnetic flux enclosed by the coil can be calculated using the formula:
ΔΦ = A * ΔB
where ΔΦ is the change in flux, A is the cross-sectional area of the coil, and ΔB is the change in magnetic field.
In this case, A = 8.5 cm^2 (which is 8.5 * 10^-4 m^2) and ΔB = 0.060 T - 0.020 T = 0.040 T.
So, the magnitude of the change in the external magnetic flux enclosed by the coil is:
ΔΦ = (8.5 * 10^-4 m^2) * (0.040 T)
(b) The average voltage induced in the coil as the external flux is changing can be calculated using the formula:
ε = -N * ΔΦ / Δt
where ε is the induced voltage, N is the number of loops in the coil, ΔΦ is the change in flux, and Δt is the time interval.
In this case, N = 200 (given) and Δt = 12 milliseconds (which is 12 * 10^-3 s).
Using the value of ΔΦ calculated in part (a), we can determine the magnitude of the average voltage induced in the coil:
ε = - (200) * [(8.5 * 10^-4 m^2) * (0.040 T)] / (12 * 10^-3 s)
(c) The magnitude of the average current in the coil can be calculated using Ohm's Law:
I = ε / R
where I is the current, ε is the induced voltage, and R is the resistance of the coil.
In this case, R = 4.0 ohms (given) and we have already calculated the value of ε in part (b). Using these values, we can determine the magnitude of the average current in the coil:
I = [(200) * [(8.5 * 10^-4 m^2) * (0.040 T)] / (12 * 10^-3 s)] / 4.0 ohms
By plugging in the given values and performing the calculations, you can find the answers to parts (a), (b), and (c) of the question.