Question

# The figure shows, in cross section, four thin wires that are parallel, straight, and very long....

The figure shows, in cross section, four thin wires that are parallel, straight, and very long. They carry identical currents of i = 2.45 A in the directions indicated. Initially all four wires are at distance d = 15.7 cm from the origin of the coordinate system, where they create a net magnetic field . (a) To what value of x must you move wire 1 along the x axis in order to rotate counterclockwise by 30°? (b) With wire 1 in that new position, to what value of x must you move wire 3 along the x axis to rotate B by 30° back to its initial orientation?

d = 15.7 cm,

current in each wire, i = 2.45 A

θ = 30o

Part a)

initially, the magnitude of the magnetic field at the origin due to each current is

B = μ0I/(2πd)

the net field is Bx = 2B = 2*μ0I/(2πd) in +ve-x-direction (due to current 2 and 4, fields due to 1 and 3 cancel each other)

move 1 to new position which is distance x from the origin,

the net field along y direction is By = μ0I/(2πx) - μ0I/(2πd)

tanθ = By/Bx

tanθ = (1/x - 1/d)/(2/d)

1/x - 1/d = 2tanθ/d

x = d/(1 + 2tanθ)

x = 7.29 cm

new position is x = -7.29 cm

Part b)

move 3 to x = +7.29 cm, then By = 0