Question

The current in a \(0.080-\mathrm{H}\) solenoid increases from \(20.0 \mathrm{mA}\) to \(160.0 \mathrm{mA}\) in \(7.0 \mathrm{s} .\) Find the average emf in the solenoid during that time interval.

Short answer

Answer: The average electromotive force (emf) in the solenoid during the given time interval is -1.6 V.

Step-by-step solution

Convert values to proper units

To work with the given values, let's convert all currents to amperes (A) and make sure all other units are in SI units. Initial current: \(I_1 = 20.0 \mathrm{mA} = 20.0 \times 10^{-3} A\) Final current: \(I_2 = 160.0 \mathrm{mA} = 160.0 \times 10^{-3} A\) Inductance: \(L = 0.080 H\) Time interval: \(\Delta t = 7.0 s\)

Calculate change in current

Calculate the change in current by subtracting the initial current from the final current: \(\Delta I = I_2 - I_1 = (160.0 - 20.0) \times 10^{-3} A = 140 \times 10^{-3} A\)

Plug values into Faraday's law formula

Plug the given values into Faraday's law formula to find the average emf: \(\text{average emf} = \frac{-L \Delta I}{\Delta t} = \frac{-(0.080 H)(140 \times 10^{-3} A)}{7.0 s}\)

Calculate the average emf

Now calculate the average emf: \(\text{average emf} = \frac{-(0.080 H)(140 \times 10^{-3} A)}{7.0 s} = -1.6 V\) The average electromotive force (emf) in the solenoid during the given time interval is \(-1.6 V\). The negative sign indicates that the emf is acting against the change in current.