Final answer:
To find the magnitude of induced emf for a change in current over time in a coil, use Faraday's Law. For a 120 mH coil with a current change from 25.0 A to 12.0 A in 350 ms, the induced emf is approximately 4.46 V.
Step-by-step explanation:
The magnitude of the induced emf in a coil can be calculated using Faraday's Law of Electromagnetic Induction, which states that the induced emf in a coil is equal to the negative change in magnetic flux (Φ) over time (t). The formula for calculating the induced emf (E) when current changes in a coil is given by E = -L (dI/dt), where L is the inductance of the coil and dI/dt is the rate of change of current.
To find the magnitude of the induced emf as the current changes steadily from 25.0 A to 12.0 A in a 120 mH coil over a period of 350 ms, we first calculate dI/dt which is change in current over change in time. dI/dt = (12.0 A - 25.0 A) / 0.350 s = -13.0 A / 0.350 s = -37.14 A/s. Since we're looking for magnitude, we take the absolute value of the result.
Now, we can calculate |E|: |E| = |- L (dI/dt)| = |-(120 x 10^-3 H) (-37.14 A/s)| = |4.4576 V| which is approximately 4.46 V to three significant figures.