Two long, straight wires cross each other perpendicularly as shown in the figure

Question

Two long, straight wires cross each other perpendicularly as shown in the figure below (let I_1 = 2.60 A, and I_2 = 5.30 A). The wires do not touch. Find the magnitude of the magnetic field at point P, which is in the same plane as the two wires. Find the direction of the magnetic field at point P. out of the page into the page 63.9degree clockwise from the +x direction 63.9degree counterclockwise from the +x direction 26.1 degree clockwise from the +x direction 26.1 degree counterclockwise from the +x direction Find the magnetic field at a point 36.5 cm above the point of intersection of the wires along the z axis; that is, 36.5 cm out of the page, toward you. Magnitude nuT direction

Explanation / Answer

Use right angle rule, the x-axis wire field at point P goes out of the page and y-axis wire field into the page.

Magnetic field due to x-axis wire is

Bx= (oi2)/(2r) = (4x10-7 x 4.5)/ (2 x 0.4) =2.25x10-6T

Magnetic field due to y-axis wire is

By = (oi1)/(2r) = (2x10-7 x 3.1)/(0.3) = 2.01x10-6T

Net magnitude of magnetic field at point P is = sqrt ((2.25x10-6)2 + (2.01x10-6)2)= sqrt(5.06x10-12 +4.04x10-12) =3.012T

b) Direction is out of page

C) distance from x-axis wire to a point Z = sqrt (0.3352+0.42) = 0.522m

BxZ= (oi2)/(2r) =(4x10-7 x 4.5)/ (2 x 0.522) = 1.72x10-6T

Similarly

distance from y-axis wire to a point Z = sqrt (0.3352+0.32) = 0.45m

By = (oi1)/(2r) = (2x10-7 x 3.1)/(0.45) =1.378x10-6 T

Net magnitude of magnetic field at point Z is = sqrt ((1.72x10-6)2 + (1.378x10-6)2)= sqrt(2.96x10-12 +1.899x10-12) =2.204T

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