100turns of insulated wire are wraped around a wooden cylindrical core of cross-sectional area 12cm2. The two ends of the wire are connected to a resistor. The total circuit resistance is 13Ω. If an externally applied uniform magnetic field along the core changes from 1.6T in one direction to 1.6T in the opposite direction, how much charge in Coulombs flows through the circuit during the change?
Pick some time over which the dB/dt takes place, say t = one second. Then dB/dt = 3.2/1 = 3.2 T/s
then you can get i for that dB/dt
then i * t = i * one second
not sure how to get i
To find the charge that flows through the circuit during the change of the magnetic field, we need to use Faraday's Law of Electromagnetic Induction. According to Faraday's Law, the induced electromotive force (EMF) is equal to the rate of change of magnetic flux through a circuit.
The magnetic flux (Φ) through a surface is given by the formula Φ = B * A, where B is the magnitude of the magnetic field and A is the area perpendicular to the magnetic field.
In this case, the cross-sectional area (A) of the wooden cylindrical core is given as 12 cm^2. We can convert this to square meters by dividing by 10,000: A = 12 cm^2 / 10,000 = 0.0012 m^2.
The change in magnetic field (ΔB) is equal to the difference between the final and initial magnetic field strengths: ΔB = 1.6 T - (-1.6 T) = 3.2 T.
The change in magnetic flux (ΔΦ) is then given by ΔΦ = ΔB * A = 3.2 T * 0.0012 m^2 = 0.00384 Wb.
Since there are 100 turns of wire, the total induced EMF in the circuit is given by ε = N * ΔΦ / Δt, where N is the number of turns and Δt is the change in time.
However, we are given the total circuit resistance (R) as 13 Ω. Using Ohm's Law, we know that the induced current (I) is given by I = ε / R.
To find the charge (Q) that flows through the circuit, we need to find the total current and multiply it by the time. Q = I * Δt.
To complete our calculations, we need to know the value of Δt. Unfortunately, the question does not provide this information, so we cannot determine the exact value of the charge flowing through the circuit.