Question

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?

Answer 1

Answer:

The charge flos through the coil is 0.023C

Explanation:

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:

$N=100$

$A= 1.32*10^{-3}m^2$

$R=15\Omega$

Where

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

The change in magnetic field can be calculated as,

$dB = 1.31-(-1.31)$

$dB = 2.62T$

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

$V = NA \frac{dB}{dt}$

In the other hand Ohm's law says:

$V = IR$

$V = \frac{dq}{dt} R$

Equating both equations we have

$\frac{dq}{dt} R = NA \frac{dB}{dt}$

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

$dq = \frac{NA(dB)}{R}$

$q = \frac{(100)(1.32*10^{-3})(2.62)}{15}$

$q = 0.023C$

Therefore the charge flos through the coil is 0.023C