Strength of a magnetic field around a wire with current

In summary, the problem involves three parallel wires with different currents flowing in opposite directions. The task is to find the strength of the magnetic field at a specific point, P, located at the "missing corner" of the square formed by the wires. Using the equation for magnetic field, the individual magnetic fields at P due to each wire are calculated and then added together, taking into account the angles of the vectors. Simple addition and subtraction do not work in this case.
  • #1
gigli
11
0

Homework Statement


Three parallel wires are arranged in a partial square configuration with point P as the fourth corner. In two of the wires at opposite corners of the square, a 5.00×10^-4 A current flows toward you, and in the third wire opposite the point P, a 7.50×10−4 A current flows away from you. The sides of the square are 5.36cm. What is the strength of the magnetic field at the point P, at the "missing corner" of the square? (T)

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Homework Equations


I believe I should be using:
(Magnetic field)=[(Permeability of free space)*(current)]/[2*pi*(distance from wire)]
The permeability of free space = (4*pi*10^-7)


The Attempt at a Solution


B1+B2-B3=BP
[(5E-4)((4*pi)E-7)]/(2*pi*.0536) = B1 = B2 = 1.9788436E-9 T

distance from wire3 and point P = r = sqrt(.0536^2+.0536^2) = .0758018469 m
[(7.5E-4)((4*pi)E-7)]/(2*pi*r) = B3 = 1.97884361E-9 T

So, B1+B2-B3 = 1.752E-9 T
which is not correct unfortunately. Do the parallel wires do something weird I am unaware of? I thought only the distance from the wire and the current determined the magnitude of the magnetic field, and the opposing currents caused opposing magnetic fields. Help!
 

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  • #2
It might help to indicate the B-field vectors at P, due to each individual wire. Be sure to draw each vector in the correct direction.
 
  • #3
I am still having trouble solving this one. Anyone have any advice?
 
  • #4
It's vector addition, where you must account for the angles of the vectors (B1, B2, and B3) you are adding up.

Simple addition & subtraction (i.e. "B1+B2-B3") does not work here.
 

What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected, such as the force exerted on a magnet or a moving electric charge.

How is a magnetic field created around a wire with current?

A magnetic field is created around a wire with current due to the flow of charged particles (electrons) through the wire. As the electrons move, they create a circular magnetic field around the wire.

What factors affect the strength of a magnetic field around a wire with current?

The strength of a magnetic field around a wire with current is affected by the amount of current flowing through the wire, the distance from the wire, and the material of the wire.

What unit is used to measure the strength of a magnetic field?

The strength of a magnetic field is measured in units of tesla (T) or gauss (G). One tesla is equal to 10,000 gauss.

How does the direction of current flow affect the direction of the magnetic field?

The direction of the magnetic field around a wire with current is perpendicular to the direction of current flow. This means that if the current is flowing upward, the magnetic field will be circling around the wire in a clockwise direction.

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