# Magnetic field outside a solenoid in 3D in terms of position

• aravindk87
In summary, the magnetic field outside a solenoid in 3D off axis can be calculated using the magnetic scalar potential, phi_m, which can be integrated from a Legendre polynomial expansion. This is the simplest method, although it can be complex.
aravindk87
Magnetic field outside a solenoid in 3D(off axis)

Hey all,
I am modeling an inductive proximity sensor and require the formula for the magnetic field just outside a solenoid off axis. In terms of a particle's position.i.e.(x,y,z). I have searched a lot of places. But most of the results show it to be zero. Please help.

Last edited:
The magnetic scalar potential, phi_m, for a single loop is given as a Legendre polynomial expansion in "Classical Electromagnetism" by Franklin.
This can be integrated to give the scalar potential for a solenoid.
That is the simplest way, but it is quite complicated.

Hello,

Thank you for your question. The magnetic field outside a solenoid in 3D can be calculated using the Biot-Savart law. The formula for the magnetic field at any point (x,y,z) outside a solenoid with a current I and radius R is given by:

B = μ0I(R^2 + z^2) / 2(R^2 + z^2)^(3/2)

Where μ0 is the permeability of free space (4π x 10^-7 N/A^2) and z is the distance from the center of the solenoid.

Off-axis, the formula becomes more complex as it also takes into account the angle of the point from the axis of the solenoid. The full formula is:

B = μ0I(R^2 + z^2) / 2(R^2 + z^2 + 2Rzsinθ)^(3/2)

Where θ is the angle between the point and the axis of the solenoid.

As you can see, the magnetic field off-axis is not zero. It is dependent on the distance from the center of the solenoid, the angle from the axis, and the current in the solenoid. I hope this helps with your modeling. Best of luck!

## 1. What is a solenoid?

A solenoid is a type of electromagnet that consists of a wire coil wound in a helical shape. It is used to generate a magnetic field when an electric current flows through it.

## 2. How does the magnetic field outside a solenoid change with position?

The magnetic field outside a solenoid is strongest at the ends and weakest at the middle. As you move away from the solenoid, the strength of the magnetic field decreases.

## 3. Does the orientation of the solenoid affect the magnetic field outside of it?

Yes, the orientation of the solenoid does affect the magnetic field outside of it. The magnetic field is strongest along the axis of the solenoid, and decreases as you move away from the axis.

## 4. How does the number of turns in the solenoid affect the magnetic field outside of it?

The number of turns in the solenoid affects the strength of the magnetic field outside of it. The more turns there are, the stronger the magnetic field will be.

## 5. Can the magnetic field outside a solenoid be manipulated?

Yes, the magnetic field outside a solenoid can be manipulated by changing the current flowing through the wire coil, changing the number of turns in the coil, or by placing other materials near the solenoid that can affect the magnetic field.

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