# Magnetic Field due to a unifrom thin current sheet of infinite extent

• Cummings
In summary, the magnetic field due to a uniform thin current sheet of infinite extent in the x-y plane with surface current density J in the positive x direction is zero.
Cummings
There is a uniform thin current sheet of infinite extent in the x,y plane.

Assuming the magnetic field is only a funtion z, perpendicular to the plane and that the magnetic field direction is parallel to the plane and perpendicular to the current direction (which is in the positive x direction)

I am asked to find an equation for the magnetic field due to the current plane using the integral form of Gauss law.

Now, all we have been taught is the magnetic field due to a current in an infinatly long wire. So, what wire would simulate this plane? I am guessing one with an infinate radius. As the magnetic field from an infinatly long straight wire does not depend on the radius, i figured that the magnetic field due to the plane is zero. Is this right? I got it using the below working.

B * 2Pi * radius of point to be measured = uI
B = uI/(2Pi * radius of point)

if the radius of the wire is infinant, then the radius of the point to be measured (in z direction) must also be infinant. This would make the magnetic field reduce to zero.

Are we on the right track? If you can't understand my working, just tell me if the magnetic field due to a infinant current plane is zero or not.

Thanks,
Cummings

Well firstly, its 'infinite'.

Second, wherever there is a moving charge, there is a magnetic field associated with that charge.

You can use the 'pillbox' Gaussian surface to find the magnetic field here, you should find this in your textbook. If it isn't under the magnetics section, try the E-field section, same basic principle.

The exact question is as follows

Use Amperes law in integral form for a static field to find an espression for the magnetic field due to a uniform thin current sheet of infinant extent in the x-y plane with surface current density J in the positive x direction. (Assume that the field strength is a function only of the perpendicular surface, z, from the sheet and that the field direction is parallel to the sheet and perpendicular to the current direction.

Cummings said:

The exact question is as follows

Use Amperes law in integral form for a static field to find an espression for the magnetic field due to a uniform thin current sheet of infinant extent in the x-y plane with surface current density J in the positive x direction. (Assume that the field strength is a function only of the perpendicular surface, z, from the sheet and that the field direction is parallel to the sheet and perpendicular to the current direction.

I think this is supposed to say

(Assume that the field strength is a function only of the perpendicular distance, z, from the sheet and that the field direction is parallel to the sheet and perpendicular to the current direction.

Given the stated symmetry, the integral form of Ampere's law involves a very simple calculation. Think about the integral for a rectangular loop cutting through the sheet.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html

## 1. What is a magnetic field due to a uniform thin current sheet of infinite extent?

A uniform thin current sheet of infinite extent is a theoretical model used to study the behavior of magnetic fields produced by a thin sheet of current that extends infinitely in all directions. This model helps scientists understand the basic principles of magnetic fields and their effects.

## 2. How is the magnetic field calculated for a uniform thin current sheet of infinite extent?

The magnetic field for a uniform thin current sheet of infinite extent can be calculated using the Biot-Savart law, which states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire. In this case, the sheet is treated as an infinite collection of parallel current-carrying wires, and the magnetic field at a point is the vector sum of the fields produced by each individual wire.

## 3. What is the direction of the magnetic field for a uniform thin current sheet of infinite extent?

The direction of the magnetic field for a uniform thin current sheet of infinite extent is perpendicular to the sheet at every point. This means that the field lines will be parallel to the sheet and will follow a circular path around each individual current-carrying wire.

## 4. How does the strength of the magnetic field vary with distance from the sheet?

The strength of the magnetic field produced by a uniform thin current sheet of infinite extent decreases as the distance from the sheet increases. This is because the magnetic field is inversely proportional to the distance from the current-carrying wires that make up the sheet. As the distance increases, the field lines spread out and become weaker.

## 5. What are some real-world applications of a uniform thin current sheet of infinite extent?

A uniform thin current sheet of infinite extent is a useful theoretical model for understanding the behavior of magnetic fields in various systems, such as electric motors, transformers, and generators. It is also used in the study of plasma physics and astrophysics to understand the behavior of magnetic fields in these environments.

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