Question

An 8-turn coil has square loops measuring 0.200 m along a side and a resistance of 3.00Ω. It is placed in a magnetic field that makes an angle of 40.0^∘ with the plane of each loop. The magnitude of this field varies with time according to B=1.50t³ , where t is measured in seconds and B in teslas. What is the induced current in the coil at t=2.00 s ?

Answer 1

The induced current in the 8-turn coil can be calculated using Faraday's law of electromagnetic induction. At t = 2.00 s, the induced current is (8 * (1.50 * (2.00)³ * 0.040)) / 3.00 amps.

Step-by-step explanation:

The induced current in the coil can be found using Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (emf) in a coil is equal to the rate of change of magnetic flux through the coil. The magnetic flux through the coil can be calculated as the product of the magnetic field and the area of each loop of the coil. In this case, the magnetic field is given by B(t) = 1.50t³ teslas and the area of each loop is 0.200 m x 0.200 m = 0.040 m². The rate of change of magnetic flux with time is then given by dΦ/dt = B(t) * A = 1.50t³ * 0.040 m². Since there are 8 loops in the coil, the total induced emf is given by ε = 8 * (dΦ/dt). To find the induced current, we divide the induced emf by the resistance of the coil. At t = 2.00 s, the induced emf is ε = 8 * (1.50 * (2.00)³ * 0.040) volts. The induced current is then given by I = ε / R = (8 * (1.50 * (2.00)³ * 0.040)) / 3.00 amps.