Question

One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area 5.87 × 10-3 m2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 14.9 Ω. If an externally applied uniform longitudinal magnetic field in the core changes from 1.93 T in one direction to 1.93 T in the opposite direction, how much charge flows through a point in the circuit during the change?

Answer 1

The amount of charge that flow through a point is
`\Delta q = 0.126 \ C`

Step-by-step explanation:

From the question we are told that

The number of turns is
`N = 100`

The area is
`A = 5.87 *10^(-3) m^2`

The total resistance is
`R = 14.9 \ \Omega`

The magnetic field in first direction is
`B_1 = 1.93 \ T`

The magnetic field in second direction is
`B_2 = -1.93 \ T`

The change in magnetic field is evaluated as

`\Delta B = B_1 - B_2`

substituting values

`\Delta B = 1.93 - [- 1.93]`

`\Delta B =3.2 \ T`

The induced emf due to the change is mathematically evaluated as

`e = NA (\Delta B )/(\Delta t )`

This can also be mathematically represented as

`e = IR`

Where I can be mathematically represented as

`I = (\Delta q )/(\Delta t)`

So

`e = (\Delta q)/(\Delta t ) R`

Now

`(\Delta q)/(\Delta t ) R = NA (\Delta B )/(\Delta t )`

=>
`\Delta q = (N A (\Delta B))/(R)`

substituting values

`\Delta q = (100 * 5.87 *10^(-3) (3.2)/(14.9)`

`\Delta q = 0.126 \ C`