Question

Two hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area 1.20 × 10−3 m2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 18.0 . If an externally applied uniform longitudinal magnetic filed in the core changes from 1.65 T in one direction to 1.65 T in the opposite direction, how much charge flows through a point in the circuit during the change?

Answer 1

Answer:

The charge flows through a point in the circuit during the change is 0.044 C.

Explanation:

Given that,

Number of turns in the copper wire, N = 200

Area of cross section, $A=1.2\times 10^{-3}\ m^2$

Resistance of the circuit, R = 118 ohms

If an externally applied uniform longitudinal magnetic filed in the core changes from 1.65 T in one direction to 1.65 T in the opposite direction.

We need to find the charge flows through a point in the circuit during the change. Due to change in magnetic field an emf is induced in it. It is given by :

$\epsilon=\dfrac{d\phi}{dt}$

Using Ohm's law :

$\epsilon=IR$

$IR=-\dfrac{d\phi}{dt}\\\\I=-\dfrac{1}{R}\dfrac{d\phi}{dt}$

Electric current is equal to the rate of change of electric charge. So,

$dq=\dfrac{NA(B(0)-B(t))}{R}\\\\dq=\dfrac{200\times 1.2\times 10^{-3}(1.65+1.65)}{18}\\\\dq=0.044\ C$

So, the charge flows through a point in the circuit during the change is 0.044 C.