A very long tightly-wound solenoid has circular cross section of radius r = 2.6
ID: 1308527 • Letter: A
Question
A very long tightly-wound solenoid has circular cross section of radius r = 2.6 cm (only a portion of the very long solenoid is shown). The magnetic field outside the solenoid is negligible. Throughout the inside of the solenoid the magnetic field B is uniform, out of the page as shown, but varying with time t: B = [0.12t - 0.06t^2] tesla. Surrounding the circular solenoid is a loop of N = 3 turns of wire in the shape of a rectangle 12 cm high by 18 cm wide. The total resistance of the 3-turn loop is 0.41 ohm.
C) At t = 0 seconds, what is the direction of the current in the 3-turn loop? Counterclockwise? there is no current in the loop? or clockwise?
D) At t = 5.5 seconds, what is the current direction in the 3-turn loop? clockwise? counterclockwise? or there is no current in the loop?
E) At t = 4.2 seconds, what is the magnitude of the current in the 3-turn loop?
F) What is the magnitude and direction of the non-coulomb electric field at the wire?
Explanation / Answer
A)flux=n. B.A
=3*(0.12t- 0.06t^2)*pi*(0.026^2)
=3.37*10^-3*(0.12t-0.06t^2)
B) dphi/dt= 3.37*10^-3*(0.12-0.12t)
C)by right hand rule, the current is clockwise
D)by right hand rule, the current is counter-clockwise.
E)magnitude of the voltage= 3.37*10^-3*(0.12-0.12*4.2)
=-1.29*10^-3 V
so current= V/R
=3.14*10^-3 A
F)direction of electric field is is the negative x direction