A long straight wire carrying a current of 2.29 A moves with a constant speed v
ID: 1440055 • Letter: A
Question
A long straight wire carrying a current of 2.29 A moves with a constant speed v to the right. A 5 turn circular coil of diameter 12.5 cm, and resistance of 3.25 , lies stationary in the same plane as the straight wire. At some initial time the wire is to the left of the coil at a distance d = 7.00 cm from its center. 9.00 s later, the wire has moved to the right of the coil and is at a distance d from the center of the coil. What is the magnitude and direction of the induced current in the coil? magnitude direction counterclockwise mA Initial situation Final situation initial situation final situationExplanation / Answer
c) Area of the loop, A = pi*d^2/4
= pi*0.015^2/4
= 1.77*10^-4 m^2
No of turns, N = 5
I = 2.29 A
t = 9 s
Let us assume magnetic filed through the loop
in the initial position
B1 = mue*I/(2*pi*d)
= 4*pi*10^-7*2.29/(2*pi*0.07)
= 6.54*10^-6 T (out of the page)
in the final position
B2 = mue*I/(2*pi*d)
= 4*pi*10^-7*2.29/(2*pi*0.07)
= 6.54*10^-6 T (in to the page)
Average induced emf = N*A*dB/dt
= 5*1.77*10^-4*2*6.54*10^-6/9
= 1.29*10^-9 volts
induced current = induecd emf/R
= 1.29*10^-9/(3.25*10^-6)
= 0.396 mA