How Does a Finite Wire Segment Affect Magnetic Field Calculation?

To find the correct equation, you need to use the Biot-Savart law, which is B = u(0)I/(4piR) * dl x r, where dl is the infinitesimal length of the wire and r is the distance from the wire element to the point where you want to find the field. In this case, you need to integrate over the entire wire segment to find the total field. In summary, to find the magnetic field at a point produced by a finite wire segment, you need to use the Biot-Savart law and integrate over the entire wire segment.
  • #1
Jethom18
2
0

Homework Statement



A long straight wire lies along the z-axis and carries an 8A current in the +z direction. Find the magnetic field (magnitude and direction) produced at x = 0.4m, y = 0, z = .3m by a .7mm segment of wire centered at the origin.

Homework Equations



B = u(0)I / 2piR

The Attempt at a Solution



b = (4(pi)x10^-7) (8A) / (2pi (.7x10^-3) ==> 2.3 mT(tesla)

I think that's right, but I'm not sure where the magnitude and direction with the vectors come in. I'm assuming you subtract vector 1 from origin vector to leave .4i + .3k. Then do you take the magnitude and multiply it by b?

Thanks for any help.
 
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  • #2
You didn't use the right equation to find B. B = u(0)I / 2piR is for an infinitely long wire, but the question asks for the field produced by a finite wire segment.
 

Related to How Does a Finite Wire Segment Affect Magnetic Field Calculation?

What is a magnetic field and how is it created?

A magnetic field is a force field that surrounds a magnetic material or a moving electric charge, causing it to experience a force. It is created by the movement of electric charges, such as in the case of a wire with electric current flowing through it.

How does the magnetic field of a wire affect nearby objects?

The magnetic field of a wire can affect nearby objects by exerting a force on them. If the object is a magnetic material, it may experience attraction or repulsion depending on the orientation of its own magnetic field. If the object is a conductor, it may experience induction and produce its own magnetic field.

What factors affect the strength of the magnetic field of a wire?

The strength of the magnetic field of a wire is affected by the magnitude of the electric current flowing through it, the distance from the wire, and the material and shape of the wire. The direction of the current also affects the direction of the magnetic field.

How can the magnetic field of a wire be measured?

The magnetic field of a wire can be measured using a device called a magnetometer. This device uses a compass or a Hall effect sensor to detect the direction and strength of the magnetic field. The unit of measurement for magnetic field is Tesla (T) or Gauss (G).

What are the practical applications of the magnetic field of a wire?

The magnetic field of a wire has many practical applications. It is used in electric motors and generators, which convert electrical energy into mechanical energy and vice versa. It is also used in magnetic resonance imaging (MRI) machines, speakers, and many other devices. Additionally, the Earth's magnetic field is essential for navigation and protection from solar wind.

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