Final answer:
The induced emf in the inductor with a current change of 1.4 A over a time of 1.0 ms is 39,200 V. It's found using Faraday's law of induction, which relates the induced emf with the rate of change of the current and the inductance.
Step-by-step explanation:
To find the induced emf in an inductor when the current is interrupted, we can use Faraday's law of induction, which states that the induced emf (ε) in an inductor is equal to the negative of the rate of change of current through the inductor times the inductance (L). The formula is given by:
ε = -L ΔI/Δt
Given that the inductance (L) is 28 henrys (H) and the change in current (ΔI) is 1.4 amperes (A) over a time interval (Δt) of 1.0 milliseconds (ms), we can calculate the induced emf as follows:
ε = -28 H * (1.4 A / 1.0 ms)
Note that 1.0 ms is equivalent to 1.0 × 10^-3 seconds. Therefore, the induced emf is calculated as:
ε = -28 H * (1.4 A / 1.0 × 10^-3 s)
= -28 × 1.4 × 10^3 V
= -39,200 V
The negative sign indicates that the induced emf is in a direction that opposes the change in current, as per Lenz's law. However, when expressing the magnitude of the emf, we can say:
ε = 39,200 volts (V)