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?
To determine the amount of charge that flows through the circuit during the change in magnetic field, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) in a closed loop is equal to the rate of change of magnetic flux through the loop.
1. First, let's calculate the magnetic flux through the loop. The magnetic flux (Φ) is defined as the product of the magnetic field strength (B) and the area (A) the field lines pass through. In this case, the area is the cross-sectional area of the wooden cylindrical core, which is given as 12 cm^2 or 0.0012 m^2.
Φ = B * A
Φ = 1.6 T * 0.0012 m^2
Φ = 0.00192 T m^2
2. Since the loop of wire consists of multiple turns, we need to consider the number of turns (N) as a factor. In this case, there are 100 turns of insulated wire.
Φ_total = N * Φ
Φ_total = 100 * 0.00192 T m^2
Φ_total = 0.192 T m^2
3. According to Faraday's law, the induced EMF (ε) is the negative rate of change of magnetic flux.
ε = -dΦ/dt
4. Finally, the amount of charge (Q) that flows through the circuit can be calculated by multiplying the induced EMF by the circuit resistance (R).
Q = ε * R
Q = -dΦ/dt * R
To find the specific amount of charge that flows through the circuit during the change in the magnetic field, we need information about the rate of change of the magnetic field (dt). Please provide any available information regarding the time interval or rate of change so that we can proceed with the calculation.