A rectangular loop of wire is placed near a long wire. The loop has has a total
ID: 1979347 • Letter: A
Question
A rectangular loop of wire is placed near a long wire. The loop has has a total resistance of 0.1 , dimensions a = 7.0 cm x b = 15 .0 cm, and is located c = 3.0 cm from the straight wire. The current in the straight wire varies as a function of time, I(t) = 9 t, where I is the current in Amps and t is the time in seconds. Determine the magnitude and direction of the induced current in the loop at t = 20 ms. (Answer in micro Amps with the convention that a positive current is ccw and a negative current is cw.)
figure shown bellow
Explanation / Answer
solved a similar question already with different numbers.. i put the question and the answer.. hope it helps!! :) kindly rate a lifesaver :)
In Figure 30-50, a rectangular loop of wire with length a, width b, and resistance R is placed near an infinitely long wire carrying current i. The loop is then moved away from the wire at constant speed v.
figure is here:
http://www.webassign.net/hrw/hrw7_30-50.gif
(Answer in terms of a, b, R, v, r, i and constants like pi and mu0 for µ0. All quantities are in SI units.)
(a) At the moment when the center of the loop is at distance r, find the magnitude of the magnetic flux through the loop.
(b) At the moment when the center of the loop is at distance r, find the magnitude of the current in the loop .
(c) What is the direction of the induced current flow?
(d) Instead of moving vertically, the loop now moves horizontally at constant speed. Find the magnitude of the induced current.
ANSWER:
B at distance r from wire is
mu0 i/(2 pi r)
flux = int [B.da] = int [mu0 i / (2pi x) a dx] from r - b/2 to r+b/2
flux = mu0 i a/2pi (ln(r + b/2) - ln(r - b/2))
current in loop I' is EMF/R
EMF = - rate of change of flux
I' = mu0 i a (b/(r^2 - b^2/4)) v/(2pi R)
as we move away from the coil the flux reduces hence the current set up will oppose this change
hence current will flow clockwise!
if loop moves horizontally there will be no change in flux...since dr/dt = 0
d flux/dt = 0
EMF = 0
I' = 0