Final answer:
To calculate the induced emf in a coil due to a changing current in a solenoid, use Faraday's law of induction and the formula for the magnetic field of a solenoid, taking into account the given solenoid dimensions, turn counts, and rate of current change.
Step-by-step explanation:
The question involves the concept of electromagnetic induction in Physics, specifically within the context of a solenoid and a coil. When the current in a solenoid changes, it induces an electromotive force (emf) in a nearby coil according to Faraday's law of induction. To find the emf induced in the coil wrapped around the solenoid, first calculate the magnetic field produced by the solenoid using the formula B = μ0 * n * I, where μ0 is the permeability of free space, n is the number of turns per unit length, and I is the current. As the current changes, the magnetic flux through the coil also changes, inducing an emf given by Faraday's law, emf = -N * dΦ/dt, where N is the number of turns in the coil and dΦ/dt is the rate of change of magnetic flux.
For the student's question, the solenoid's length, diameter, number of turns, and the rate at which the current increases, along with the turns in the coil, are provided. Using these values and Faraday's law, one can calculate the induced emf in the 17-turn coil wrapped around the solenoid as the current increases uniformly from 0 to 6.1 A over 0.70 seconds.