An infinite straight wire carries current I 1 = 2 A in the positive y-direction
ID: 2120869 • Letter: A
Question
An infinite straight wire carries current I1 = 2 A in the positive y-direction as shown. At time t = 0, a conducting wire, aligned with the y-direction is located a distance d = 75 cm from the y-axis and moves with velocity v = 17 cm/s in the negaitve x-direction as shown. The wire has length W = 26 cm.
1.) The wire is now replaced by a conducting rectangular loop as shown. The loop has length L = 59 cm and width W = 26 cm. At time t = 0, the loop moves with velocity v = 17 cm/s with its left end located a distance d = 75 cm from the y-axis. The resistance of the loop is R = 1.1 %u03A9. What is i(0), the induced current in the loop at time t = 0? Define the current to be positive if it flows in the counter-clockwise direction.
2.)Suppose now that the loop is rotated 90o and moves with velocity v = 17 cm/s in the positive x-direction as shown. What is I2, the current in the infinite wire, if the induced current in the loop at the instant shown (d = 75 cm) is the same as it was in the third part of this problem (i.e., when the left end of loop was at a distance d = 75 cm from the y-axis)?
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Explanation / Answer
1)the induced emf is
E = (dO/dt)
where dO = B x A,B is magnetic field and A = L x W and dt is time
we know that
E = I x R
where I is induced current and R is resistance
or I = (E/R)
2)the force between the wire and loop is
F = (u_o x I1 x I2/2pi x d) x L
here,F = (mv^2/d)
where m is mass of loop and v is its velocity
from the above two equations we get the value of I2