One hundred turns of insulated copper wire are wrapped around an iron core of cross-sectional area 0.100 m². The circuit is completed by connecting the coil to a 10- $\pi$ resistor. As the magnetic field along the coil axis changes from 1.00 T in one direction to 1.00 T in the other direction, the total charge that flows through the resistor is:

Question

Quizplus · Accepted Answer

The induced emf in the coil is given by:
emf = -N(dΦ/dt),
where N is the number of turns in the coil and Φ is the magnetic flux through the coil.

The magnetic flux through the coil is proportional to the magnetic field intensity and the cross-sectional area of the core:
Φ = B*A = (1.00 T)(0.100 m^2) = 0.100 Wb.

Since the magnetic field changes from 1.00 T in one direction to 1.00 T in the other direction, the change in magnetic field intensity is ΔB = 2.00 T. The time for this change to occur is not given, but we can assume that it happens instantaneously.

Then, the induced emf is:
emf = -N(dΦ/dt) = -N(ΔB/Δt) = -100(2.00 T/Δt) = -200/Δt V.

The current that flows through the circuit is given by Ohm's law:
I = V/R = (200/Δt)/(10 Ω) = 20/Δt A.

The total charge that flows through the circuit is given by:
Q = ∫I dt = I*Δt = (20/Δt)(Δt) = 20 C.

Therefore, the best choice is D) 2 C.

One Hundred Turns of Insulated Copper Wire Are Wrapped Around π\piπ

One Hundred Turns of Insulated Copper Wire Are Wrapped Around $\pi$