Four very long wires are directed perpendicular to the plane of the figure below

Question

Four very long wires are directed perpendicular to the plane of the figure below. The points where these wires cross the plane of the drawing form a square of edge length 0.55 m, and each wire carries a current of magnitude 3.3 A. Find the magnetic field at the center of the square (i.e., at the origin).

direction

Four very long wires are directed perpendicular to the plane of the figure below. The points where these wires cross the plane of the drawing form a square of edge length 0.55 m, and each wire carries a current of magnitude 3.3 A. Find the magnetic field at the center of the square (i.e., at the origin). Four very long wires are directed perpendicular to magnitude T [5 points] 1 attempt(s) made (maximum allowed for credit = 5) 1.433E-5 NO direction [5 points] 0 attempt(s) made (maximum allowed for credit = 1)

Explanation / Answer

Suppose the wire are arranged as:
A B

C D
where the currents in A and D are in the same direction (both up or both down)
and the currents in B and C are in opposite directions (one up, the other down).

The fields from A and D cancel (use the right hand rule to get their directions at the centre of the square and you will see they are opposite).

The fields from B and C add as vectors in the same direction (simple addition of magnitudes).

The centre of the square is a perpendicular distance r = 0.6/2 = 0.3m from each wire

The magnitude of the field from one wire at the centre is B where
B = ??I/(2?r)
= 4?x10?? x 3.3 (2? x 0.55/2)
= 7.165x10?? T

So the magnitude at the centre (due to B and C) is 2 x 7.165x10?? = 1.433x10?? T

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