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?

Question

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?

Answer 1

To calculate the charge that flows through the circuit during the change in the magnetic field, we need to consider Faraday's Law of electromagnetic induction. According to Faraday's Law, when the magnetic field through a loop changes, an electromotive force (emf) is induced in the loop, causing a current to flow.

The formula for calculating the induced emf is:
emf = -N * A * dB/dt,

where
emf is the induced electromotive force,
N is the number of turns of wire,
A is the cross-sectional area of the loop, and
dB/dt is the rate of change of the magnetic field.

In this case, we are given:
Number of turns, N = 100,
Cross-sectional area, A = 12 cm^2 = 0.0012 m^2 (converted from cm^2 to m^2),
Change in magnetic field, dB = 1.6 T - (-1.6 T) = 3.2 T (since the field changes from 1.6 T in one direction to -1.6 T in the opposite direction).

Now, let's calculate the induced emf using the given values:
emf = -N * A * dB/dt
= -100 * 0.0012 * 3.2
= -0.384 V.

Since the resistance of the circuit is given as 13 Ω, we can use Ohm's Law (V = I * R) to find the current that flows through the circuit:
0.384 V = I * 13 Ω.

Rearranging the equation, we find:
I = 0.384 V / 13 Ω
≈ 0.02954 A.

Now that we have the current, we can calculate the charge that flows through the circuit during the change in the magnetic field. The charge can be found using the equation Q = I * t, where Q represents charge, and t represents time. However, we currently don't have the value of time given in the question. Without the time, we cannot calculate the charge accurately.

Hence, we cannot find the exact amount of charge in Coulombs that flows through the circuit during the change in the magnetic field without knowing the time.