The figure shows in cross section four thin wires that are p

The figure shows, in cross section, four thin wires that are parallel, straight, and very long. They carry identical currents of i = 2.75 A in the directions indicated. Initially all four wires are at distance d = 17.7 cm from the origin of the coordinate system, where they create a net magnetic field B.(a) To what value of x must you move wire 1 along the x axis in order to rotate B counterclockwise by 30degree? (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 30degree back to its initial orientation? (a) Number Units (b) Number Units

Solution

given that,

distance: d = 17.7 cm,

current in each wire = I = 2.75 A,

angle: = 30^o
the magnitude of the magnetic field:

B = ₀I/(2d)
the net field is:

B_x = 2B

=2*₀I/(2d) in +x direction
the netfield along y direction is:

B_y =₀I/(2x) - ₀I/(2d)

tan = B_y/B_x
tan = (1/x - 1/d)/(2/d)
1/x - 1/d = 2tan/d
therefore,

x = d/(1 + 2tan) = 8.21 cm
answer: new position is x = -8.21 cm = -0.0821 m

b) move 3 to x = +8.21 cm = 0.0821 m, then B_y = 0.