Question

One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area 3.02 × 10-3 m2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 14.3 Ω. If an externally applied uniform longitudinal magnetic field in the core changes from 1.88 T in one direction to 1.88 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 circuit is
`7.94 * 10^(-2)` C

Step-by-step explanation:

Given:

Cross-sectional area
`A = 3.02 * 10^(-3)`
`m^(2)`

Resistance
`R =` 14.3Ω

Magnetic field
`B = 1.88` T

According to the faraday's law

Induced emf is given by,

`\epsilon = -(d\phi)/(dt)`

The induced current is given by,

`I = (\epsilon )/(R)`

`I = -(d\phi)/(Rdt)`

`(dq)/(dt) = -(d\phi)/(Rdt)`

`dq = (d\phi)/(R)`

Where
`d\phi = A (B_(0) - B_(t) )`

`B_(0) = 1.88` and
`B_(t) = -1.88`

`dq = (3.02 * 10^(-3) * 3.76 )/(14.3)`

`dq = 7.94 * 10^(-2)` C

Therefore, the charge flows through a point in circuit is
`7.94 * 10^(-2)` C