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

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

Step-by-step explanation:

Given that,

Number of turns in the copper wire, N = 200

Area of cross section,
`A=1.2* 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=(d\phi)/(dt)`

Using Ohm's law :

`\epsilon=IR`

`IR=-(d\phi)/(dt)\\\\I=-(1)/(R)(d\phi)/(dt)`

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

`dq=(NA(B(0)-B(t)))/(R)\\\\dq=(200* 1.2* 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.