Two infinitely long current carrying wires are separated by a distance of 0.3m.

Question

Two infinitely long current carrying wires are separated by a distance of 0.3m. The point of interest P is at a distance of 1.2m from the closest wire as hown in the figure below. The two current carryin wires are perpendicular to the page. The symbol X means the current is flowing into the page and the symbol O means teh current is flowing out of the paper. The current that is flowing into the paper is 3.0 A. The net magnetic field at point P is 3.33 x 10-7 Tesla and its direction is toward the bottom edge of the paper.

* - - - - - - - - - - - - - - - - - - -X - - - - - - - - O

(P)   1.2 m     (3.0 A)  0.3 m   (I)

A) Draw in the figure below a single vector (arrow) to represent the direction of the magnetic field due to the current in the wire that is closest to the point P.

* - - - - - - - - - - - - - - - - - - -X - - - - - - - - O

B) Find the current I in the farthest wire from point P so that the net magnetic field due to both wires is 3.33 x 10-7 Tesla, pointing toward the bottom edge of the paper.

C) Find the magnitdue and the direction of the net magnetic field at point P if the direction of the current I in the farthest wire from point P is reversed.

Please describe in detail how you find your solutions.

Explanation / Answer

According to the question

We know that

a.) By right hand rule, take your right hand and point your thumb into the page, your fingers curl clock wise. this means if you draw a clockwis circle around the wire through point p, the tangent direction of the arrow would be up. So the direction of your magnetic field due to the wire into the page is up.

Then,

b.) The b field due to a wire is mewnot * i / (2 * pi * r), mewnot = 4 pi *10^-7

since the wire into page has a current of 3A and is 1.2 m away its b-field is 5*10^-7 tesla in the upward direction. the problem asks for the current of the other wire into the page so that combined the b-fields equal 3.33*10^-7 downward, meaning the b-field of that wire must be 8.33*10^-7 downward, using the same equation again and plugging in b and r, doing a little algebra gives you

i = 6.247 A

Then,

c.) If the furthest current was reversed to into of the page, then then both b-fields would be upward yielding a magnitude of 13.33*10^-7

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