Question

4) Induction Effect. A very long solenoid of radius R-2.5 cm has n 5 turns/cm. Starting from an initial current of io 50 A at 1 = 0, a steadily increasing current is driven through the coils of the solenoid, at a rate of didt = 10 A/s. The solenoid is surrounded by a square flat "pickup" coil of N= 100 turns and of side lengthに10 cm (oriented with its plane perpendicular to, and its center at, the solenoid axis). a) At 2 s, what is the magnetic flux through the pickup coil? b) What is the rate of change of magnetic flux through the pickup coil? c) What is the magnitude of the induced EMF across the terminals of the pickup coil? 5 s, the current in the solenoid reaches its maximum value of 100 A and becomes constant at that value. d) What is the magnitude of the induced EMF in the pickup coil after this time? e) Graph i versus time and the induced EMF magnitude versus time, from 0 to 10 s. At t Reflect on the graph: what is required, in order to produce an induced EMF in the pickup coil? How does Faraday's Law show this relationship?

Answer 1

Ho) The mametic flux through the ct uメ Yov Aニarea otthe cross-section os the solenoid [as magnetic ield is in his region only) 2. 兀 B magnetic field at the center of the holenoid, -current in the solenoid n= no turns er meter dt dt dt at t 24 Crn putting these into #Oto get φ at t=2.5 ) Th thro e rate oj change in magnetic flux the pickup coil clt

d七 of change of fi«Kal=4.RNnRač dt dt i c) The maghitude of the induced ef d-t =k23 XiGU) The ma gnitude of the emf yce a) Since thef change of the curvent e Curfen o after t- Ss magnitude of the emf induce d IA [00 -3 1.25% lo

In order to produce an induced EMF, the change in the current in the solenoid is required. Faraday's law shows this relationship with the change in the magnetic flux through the pickup coil.