2) (10 pt) A very long solenoid has a circular cross section of radius r=4 cm. T

Question

2) (10 pt) A very long solenoid has a circular cross section of radius r=4 cm. The magnetic field outside the solenoid is zero. Inside the solenoid the magnetic field B is uniform, out of the page, and varies with time; the magnetic field strength changes uniformly from 0 at t=0 seconds to B=2.2 tesla at t=4 seconds. Surrounding the solenoid is a rectangular loop of wire with 4 turns and 10cm high and 15cm wide. The total resistance in the 4 turn wire is 1.5 ohms. (a) What direction is the current induced in the 4 turn loop t=4 seconds later? (clockwise or counter-clockwise looking through the loop.) (b) What is the emf induced in the 4 turn loop? (c) What is the magnitude of the current in the 4-turn loop? 13 3)A proton is moving in a circle of radius R at constant speed, perpendicular to a uniform magnetic field. The proton makes one clockwise revolution every 120 nanoseconds (see the figure). If the speed is small compared to the speed of light, what is the magnitude and direction of the magnetic field?

Explanation / Answer

a]B = 0 at t= o

B = 2.2 at t = 4 s

so the magnetic field is increasing with time t out of the plane

so this increase in magnetic field field will induce a current in the coil and the curent will be in such a direction that it will try to balance the increase in magnetic field so the effect of the induced current should be into the plane so the diirection of current should be clockwise direction

b] the emf induced in the coil = NA dB / dt

= 4* [ 0.1*0.15] [ 2.2-0] / [ 4-0]

= 0.033V

c] the current induced = Emf induced = Iinduced * R

= 0.033/ 1.5 = I induced

= 0.022 A

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