Question

Learning Goal:

To practice Problem-Solving Strategy 32.1 The magnetic field of a current.

A long wire carries current I. The wire is straight except for one square-shaped "half-loop" KLMN as shown.(Figure 1) Find the magnitude and the direction of the magnetic field B? at point P. Assume that d is a known quantity.

Find the magnitude of magnetic field Bnet

Express your answer in terms of some or all of the quantities d and I, and the constants ?0 and ?.

Answer 1

There is no magnetic field due to JK segment at point P
magnetic field due to KL segment
B1 = u0*I[sina+sinb]/(4pi*r)
sin a = d/sqrt(5d^2/4) = 2/sqrt(5)
r = d/2
so B1 = 2u0*I/2pi*dsqrt(5)= u0*I/(pi*d*sqrt(5))
magnetic field due to MN segment is also same
B1 = B3 = u0*I/(pi*d*sqrt(5))
magnetic field due to LM segment
B2 = u0*I/(2pi*d*sqrt(5))
so Bnet = B1+B2+B3 = u0*I/(pi*d*sqrt(5))[2+0.5] = u0*I*sqrt(5)/(2pi*d)
direction is in to the plane of the loop