One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area 1.32 × 10-3 m2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 10.6 Ω. If an externally applied uniform longitudinal magnetic field in the core changes from 1.31 T in one direction to 1.31 T in the opposite direction, how much charge flows through a point in the circuit during the change?

To solve this problem, it is necessary to apply the concepts related to Faraday's Law in which it is possible to calculate the emf Voltage induced due to a charge in a magnetic field

and Ohm's Law for the calculation of the current based on a given load over time.

Our data are given by:

[tex]N=100[/tex]

[tex]A= 1.32*10^{-3}m^2[/tex]

[tex]R=15\Omega[/tex]

Where

N is the number of loops, A the area and R the Resistance.

The change in magnetic field can be calculated as,

[tex]dB = 1.31-(-1.31)[/tex]

[tex]dB = 2.62T[/tex]

The Faraday's law of electromagnetic induction is given by definition as,

[tex]V = NA \frac{dB}{dt}[/tex]

In the other hand Ohm's law says:

[tex]V = IR[/tex]

[tex]V = \frac{dq}{dt} R[/tex]

Equating both equations we have

[tex]\frac{dq}{dt} R = NA \frac{dB}{dt}[/tex]

We can re-arrange the equations to solve q, then

[tex]dq = \frac{NA(dB)}{R}[/tex]

[tex]q = \frac{(100)(1.32*10^{-3})(2.62)}{15}[/tex]

[tex]q = 0.023C[/tex]

Therefore the charge flos through the coil is 0.023C