Magnetic Field of Two Wires

In summary, the question asks for the magnitude of the magnetic field at the center point given the values of r, i, and i'. Using Biot-Savart's law, the magnetic field for i and i' are calculated and added together to get the total magnetic field. The correct equation for Biot-Savart's law for a loop is u*I/4*R, and since only half a loop is considered, the total magnetic field is equal to u*I/2*R. Plugging in the given values and solving, the correct magnitude of the magnetic field at the center point is obtained.
  • #1
ttiger2k7
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[SOLVED] Magnetic Field of Two Wires

Homework Statement



http://img80.imageshack.us/img80/5625/jonesj2qm4.gif

If r = 30.0 mm, i = 2.00 A, and i' = 8.60 A, what is the magnitude of the magnetic field at the center point?

Homework Equations



B=([tex]\mu[/tex][tex]_{0}[/tex]I)/(2pi*r)

The Attempt at a Solution



I applied biot-savart's law to i and i', and added them together.

For B_i:

(4pi*10^-7*2)/(2pi*.03) = 1.34*10^-5

For B_i':
(4pi*10^-7*8.6)/(2pi*.03) = 5.74*10^-5

B_center = B_i + B_i' = 7.08*10^-5

Which is not correct. I'm pretty much sure my method at solving the problem is completely wrong. I just don't know what exactly is the right steps to take. Any help would be appreciated.
 
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  • #2
biot-savart for a loop is u*2*pi*I/4*pi*R, which simplifies to u*I/2*R.. you're only looking for half a loop so 1/2 * that is equal to u*I/4*R ..

The total mag field would thus be: u*I'/4*R + u*I/4*R

u = 4*pi*10^-7, by the way.
 
Last edited:
  • #3
Ah, thanks! Got it.
 

1. What is a magnetic field?

A magnetic field is a region of space around a magnet or electric current where magnetic forces can be observed. It is represented by lines of force that show the direction and strength of the magnetic field.

2. How do two wires create a magnetic field?

When two wires with electric current flowing in the same direction are placed parallel to each other, they create a magnetic field that interacts with each other. This is known as the "right-hand rule" where the fingers of your right hand point in the direction of the current and your thumb points in the direction of the magnetic field.

3. What is the direction of the magnetic field between two wires?

The direction of the magnetic field between two wires is perpendicular to the wires and in the same direction as the current flow. This means that the magnetic field lines are circular around each wire and intersect in the space between them.

4. How does the distance between two wires affect the strength of the magnetic field?

The strength of the magnetic field between two wires is directly proportional to the distance between them. As the distance increases, the strength of the magnetic field decreases. This is because the magnetic field lines spread out over a larger area, resulting in a weaker field.

5. What is the application of the magnetic field of two wires?

The magnetic field of two wires has various applications, such as in electromagnets, motors, and generators. It is also used in medical imaging, such as MRI machines, and in electronic devices like speakers and headphones.

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