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

The charge flos through the coil is 0.023C

Step-by-step 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 (dB)/(dt)`

In the other hand Ohm's law says:

`V = IR`

`V = (dq)/(dt) R`

Equating both equations we have

`(dq)/(dt) R = NA (dB)/(dt)`

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

`dq = (NA(dB))/(R)`

`q = ((100)(1.32*10^(-3))(2.62))/(15)`

`q = 0.023C`

Therefore the charge flos through the coil is 0.023C