The figure below shows four parallel wires arrayed at the indicated coordinates

Question

The figure below shows four parallel wires arrayed at the indicated coordinates in the xy plane carrying identical currents of 1.83 A. The currents in wires A and B are in the positive z direction (out of the page), and the currents in wires C and D are in the negative z direction (into the page). What are the magnitude and direction of the magnetic field at the origin? 1,036 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. T magnitude direction 50.0cm, 50.0 cm) (S50.0 cm, 50.0cm) -50.0cm,50.0 cm) (50.0 cm,-50.0 cm)

Explanation / Answer

Given  

I = 1.83 A

four wires are at four corners of a square with side of 1 m , and origin is at (0m,om)

now the by right hand rule the magnetic field at origin due to upper wires is into the page and  

due to lower left wire into the page and right corner wire out of the page with equal magnitudes, so lower wires magnetic field at origin cancels

the magnetic field is B = mue0*i/2pi*r

here mue0 = 4pi*10^-7 , r = sqrt(0.5^2+ 0.5^2) = 0.71 m

B = B1+B2

B = -(mue0*i/2pi*r+mue0*i/2pi*r)

B= -2*mue0*i/2pi*r

B = -2*4pi*10^-7*8.3/2pi*0.71)

B = 1.8867*10^-6 T

the direction is into the page -z direction

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