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

ID: 2260172 • Letter: F

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 0.52 m, and each wire carries a current of magnitude 3.5 A. Find the magnetic field at the center of the square (i.e., at the origin).

magnitude=

direction=

Explanation / Answer

At the centre, there are 4 fields with (possibly) different directions. The fields have to be added by vector addition. To get the direction of each field you use use the right hand rule (see link). You haven't given the directions of the currents, so it is not possible to explain how to do this bit in detail.

Here's an EXAMPLE to show the method. Check you own question and repeat with the actual current directions.

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 = 0.52/2 = 0.26m from each wire

The magnitude of the field from one wire at the centre is B where
B = ??I/(2?r)
= 4?x10?? x 3.5(2? x 0.3)
= 2.33x10?? T

So the magnitude at the centre (due to B and C) is 2 x 2.33x10?? = 0.466x10?? T

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

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

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