How do you calculate magnetic field stregth outside a solenoid?

[rsalmon]

Hi,

I've have been searching for help in calculating the magnetic field strength at any given position outside a solenoid.
I can use Biot-Savart's to get the field along the axis of the solenoid but how does the field vary perpendicular to the axis of the solenoid, for example.

Rob

 

[Bob S]

The vector potential and the components of the field everywhere outside a single current loop is given by Smythe Static and Dynamic Electricity Third Edition, page 291, in terms of elliptic integrals. The field of a multiturn solenoid can be calculated using numerical integration. The fields can also be calculated using expressions involving Legendre polynomials on pages 293-4. I cannot find any closed-form expression for the off-axis field for a multi-turn solenoid. The on-axis field is given by the closed-from expression

http://www.netdenizen.com/emagnet/solenoids/thinsolenoid.htm

Bob S

 

[rsalmon]

Ok thanks Bob,
I had a look at the text and this is going to call for a simple(ish) computer code. In fact I have found a magnetic field calculator at this site

http://vizimag.com/calculator.htm

This says it does the fields outside and off axis. though haven't tried it yet, waiting for admin to let me install it.

Thanks again. Rob

 

[Bob S]

Rsalmon-
The equation for the magnetic field near an aircore solenoid used by Visimag seems to be correct. It uses both elliptic integrals E(θ) and K(θ), as shown in Smythe. The series expansions for these elliptic integrals are in Dwight Tables of Integrals (Macmillan, 1947), paragraphs 773 and 774 on page 171. The recursion formulas for these series expansions are simple, and the integrals can be easily evaluated in a short subroutine.

Bob S

 

[sardar]

ust calculations of magnetic field strength outside a solenoid can be done using the formula:

B = μ0 * n * I

Where B is the magnetic field strength, μ0 is the permeability of free space (4π x 10^-7 H/m), n is the number of turns per unit length of the solenoid, and I is the current flowing through the solenoid.

To calculate the field strength at a specific point outside the solenoid, we can use the right-hand rule to determine the direction of the magnetic field. Then, we can use the formula above to calculate the magnitude of the field.

It is important to note that this formula assumes that the solenoid is infinitely long and has a uniform current distribution. In real-world situations, the field may vary due to imperfections in the solenoid's construction or non-uniform current distribution.

Additionally, to calculate the field strength at a point inside the solenoid, we can use the formula:

B = μ0 * n * I * (cosθ1 - cosθ2)

Where θ1 and θ2 are the angles between the axis of the solenoid and the line connecting the point to the end of the solenoid.

In summary, calculating the magnetic field strength outside a solenoid involves using the Biot-Savart law and taking into account the number of turns per unit length and the current flowing through the solenoid. It is important to also consider the assumptions and limitations of the formula in real-world scenarios.