Question

The magnetic flux through each turn of a 170-turn coil is given by phi_ = 9.75 times 10⁻³ sin (omega t), where omega is the angular speed of the coil and phi_B is in webers. At one instant, the coil is observed to be rotating at a rate of 8.50 times 10² rev/min. (Assume that t is in seconds) (a) What is the induced emf in the coil as a function of time for this angular speed? (Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that element is in volts. Do not include units in your answer.) (b) What is the maximum induced emf in the coil for this angular speed?

Answer 1

The induced emf in a coil can be found using the derivative of magnetic flux with respect to time multiplied by the number of turns. For maximum emf, omega should be converted to rad/s and multiplied by the maximum value of the sine function along with the number of turns.

Step-by-step explanation:

The student is asking about the induced electromagnetic force (emf) in a rotating coil within a magnetic field, which can be calculated using Faraday's law of electromagnetic induction. For a 170-turn coil with the magnetic flux Φ = 9.75 x 10⁻³ sin(omega t), the induced emf (e) as a function of time would involve the derivative of the magnetic flux with respect to time and multiplying it by the number of turns in the coil (N). The calculation would look like this: e = -N * dΦ/dt. Given an angular speed (omega) in rev/min, one would first convert it to rad/s since omega in the given phi function is in terms of rad/s.

To find the maximum induced emf, the student would need to determine the maximum rate of change of phi, which occurs when sin(omega t) = ±1, meaning the emf is at its peak positive or negative value. The peak value can then be calculated using the maximum value of the sine function (1) while taking into account the negative sign due to Lenz's Law.