Question

Two long, straight wires are separated by 2 m with wire 1 being on the left and wire 2 being on the right. Both wires carry currents of 8.5 A in opposite directions. Find the magnitude of the net magnetic field: a) 4 m to the left of wire 1 BL= __________ T b) In the middle, between both wires BM = __________ T c) 4 m to the right of wire 2 BR = __________ T

Answer 1

a)

r = distance between the two wires = 2 m

r₁ = distance of wire 1 from the point = 4 m

r₂ = distance of wire 2 from the point = r + 4 = 2 + 4 = 6 m

magnetic field by wire 1 is given as

B₁ = (/4) (2i/r₁) in outward direction

magnetic field by wire 2 is given as

B₂ = (/4) (2i/r₂) in inward direction

Net magnetic field is given as

B_L = B₁ - B₂ = (/4) (2i/r₁) - (/4) (2i/r₂)

B_L = (/4) (2i) (1/r₁ - 1/r₂ )

B_L = (10^-7) (2(8.5)) (1/4 - 1/6​​​​​​​ )

B_L = 1.42 x 10^-7 T

b)

r = distance between the two wires = 2 m

r₁ = distance of wire 1 from the middle point = 1 m

r₂ = distance of wire 2 from the middle point = 1 m

magnetic field by wire 1 is given as

B₁ = (/4) (2i/r₁) in inward direction

magnetic field by wire 2 is given as

B₂ = (/4) (2i/r₂) in inward direction

Net magnetic field is given as

B_M = B₁ + B₂ = (/4) (2i/r₁) + (/4) (2i/r₂)

B_M = (/4) (2i) (1/r₁ + 1/r₂​​​​​​​ )

B_M = (10^-7) (2(8.5)) (1/1 + 1/1​​​​​​​ )

B_M = 3.4 x 10^-6 T

c)

r = distance between the two wires = 2 m

r₁ = distance of wire 1 from the point = r + 4 = 2 + 4 = 6 m

r₂ = distance of wire 2 from the point = 4 m

magnetic field by wire 1 is given as

B₁ = (/4) (2i/r₁) in inward direction

magnetic field by wire 2 is given as

B₂ = (/4) (2i/r₂) in outward direction

Net magnetic field is given as

Net magnetic field is given as

B_R = B₂ - B₁ = (/4) (2i/r₂) - (/4) (2i/r₁)

B_R = (/4) (2i) (1/r₂ - 1/r₁​​​​​​​ )

B_R = (10^-7) (2(8.5)) (1/4 - 1/6​​​​​​​ )

B_R ​​​​​​​= 1.42 x 10^-7 T