Question

Consider two wires carrying currents i in rate following arrangement. We want to fine me magnetic field (magnitude and direction) of point P. we will use super position and symmetry arguments to find me magnetic field at point P, as well as mp fact that me magnetic field at a distance r from an infinite current carrying wire is B = mu_o i/2 pi r A) What is the magnetic field due to the semi-infinite wire AB? B) What is the magnetic field due to the semi-infinite wire CD? C0 What is the direction of the magnetic field due to wire BC? D) What is the direction of the magnetic field due to wire F6? E) How do the magnitudes of me magnetic field due to wires BC and F6 compare? F) What is the magnetic field due to semi-infinite wire EF? G) What is the magnetic field due to semi-infinite wire GH? Putting together the above information, what is the total magnetic field (magnitude and direction) at point P?

Answer 1

The units of r is not mentioned. I have assumed it to be cm.

Current if flowing (D to A) and (H to E)

B_AB = μ₀I / 2πr = (4π*10^-7)(250) / (2*π*0.15) = 3.34*10^-4 T (Direction: out of the plane of paper)

B_CD = μ₀I / 2πr = (4π*10^-7)(250) / (2*π*0.15) = 3.34*10^-4 T (Direction: out of the plane of paper)

Magnetic field due to circular wire at center = μ₀I / 2r

Magnetic field due to quarter-circular wire at center = (1/4)(μ₀I / 2r) = μ₀I / 8r

B_BC = μ₀I / 8r = 1.05*10^-6 T (Direction: out of the plane of paper)

B_FG = μ₀I / 8r = 1.05*10^-6 T (Direction: into of the plane of paper)

B_EF = B_GH = 0

Net magnetic field at point P = B_AB + B_CD + B_BC - B_FG = 6.6*10^-4 T (Direction: out of the plane of paper)