Question

$h16_BfromWire$

An infinite straight wire carries current I₁ = 3 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 = 41 cm from the y-axis and moves with velocity v = 18 cm/s in the negaitve x-direction as shown. The wire has length W = 28 cm.

1)What is ε(0), the emf induced in the moving wire at t = 0? Define the emf to be positive if the potential at point a is higher than that at point b.V

2)What is ε(t₁), the emf induced in the moving wire at t = t₁ = 1.5 s? Define the emf to be positive if the potential at point a is higher than that at point b.V

3)

$h16_BfromWireC$

The wire is now replaced by a conducting rectangular loop as shown. The loop has length L = 42 cm and width W = 28 cm. At time t = 0, the loop moves with velocity v = 18 cm/s with its left end located a distance d = 41 cm from the y-axis. The resistance of the loop is R = 1.7 Ω. 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.A

4)

$h16_BromWireD$

Suppose the loop now moves in the positive y-direction as shown. What is the direction of the induced current now?

The current flows counterclockwise

The current flows clockwise

There is no induced current now

5)

$h16_BfromWireE$

Suppose now that the loop is rotated 90^o and moves with velocity v = 18 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 = 41 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 = 41 cm from the y-axis)?

Answer 1

Mgnec feld ue to I, at the distante &from the wire, MOLI b2Rd Motional emb is definat as, eketomotive fone nduel in the wre length W, We get, E= VBW |MOI b E = V (2Ã. MOIV W E = 1 67aling fight hank ruule we Can bink the voltage at o weuld a be grester thm b, then -V,= >V

(4XXA)(4 4)(0-13 |s) (0 - 2») V-V, b Q (0-41m) VA-V7.38Xi0v) A b). at t=1-5&% Yod =Xvt distane tavele distane of td ton wire = d2 d- ut d41m-(3ss9 O -1MM da= 14cm Magnche fo t (axid]mh)(an) b = 2x (0- 14m).

b=4-286x Now, V- BW Va-Vi=b+m{[4 286s6f (20m) V2-V1=|2.16x1V A