Magnetic field outside solenoid

electromagnetismmagnetics

It is written in our course book that the magnetic field outside a solenoid is negligible and almost zero. Why is it negligible? Is it negligible compared to the field inside solenoid or is it nearly equal to zero?

Best Answer

A simple model to help you visualize: The magnetic flux forms loops, you cannot have a magnetic field line terminate on nothing in free space. That means that all those flux lines inside the solenoid heading (for example) to the right. The flux line must continue outside the solenoid and loop around to join the other end of the flux loop. In doing so it heads to the left. No external flux lines -> no flux.

So what could be the issue?

1) In an infinite solenoid, there is no external magnetic field. One example of this is a Tokamak or toroidal solenoid. Like a big doughnut. The flux lines form loops within the doughnut and have no need to go outside. - of course a mathematically ideal infinite solenoid could have been what they were discussing, in which case the field lines loop around infinity. Hard to test though.

2) The flux density outside of the linear finite solenoid is much less than inside. So while there may be X flux across the throat of the solenoid that same amount of flux (X) is spread out over a much much larger cross sectional area. The density is much less. [here the area is the cross sectional area across the solenoid.]

3) Perhaps they are talking about a shielded solenoid? This would involve having a high permittivity material external to the coils to trap the flux lines.

Related Solutions

Electronic – Amperian loop to measure solenoid’s magnetic field

If you could do that, then you could also superimpose the contributions from the vertical plane (the plane normal to the sheet of paper) to get B=4μ0In. Or again at every degree around the coil for B=360μ0In. Which would be ridiculous.

Instead, if you look at that row of conductors within the orange loop, consider that it is symmetrical; the field below it and the field above it (from the infinitesimally thin sliver of conductor passing through the paper alone) would be identical. (Correction : the magnitude would be identical; the direction would not!)

Integrate the field from all those slivers around the entire coil and the total field inside the coil is B=μ0In. There are exactly as many "lines of flux" outside the coil, but distributed over a much larger area (theoretically extending to infinity), so the external magnetic field is relatively low.

Electronic – Can a solenoid have its magnetic field “focused”

In short NO.

A solenoid would produce a field similar to what you show in the second "picture". The only difference you could make would be to increase or decrease the amplitude of that field (or make it negative). Although this field is for the most part inside the solenoid (not the outside).

The simplest way to do something similar to what you're after would be to split the coil into two. Then alter their amplitudes so that you get maximums or null fields where ever you want with relation to the center of both of those coils by simply changing the magnitude and direction of either coil. Using 2 PWMs with simple filters and 2 solenoids you could accomplish pretty much what you're after.

It would look something more like this:

////////////   ////////////////  
     <       ~~~       >                            
////////////   ////////////////

Where the field can be "moved" anywhere between the two greater/less than signs.

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Related Solutions

Electronic – Amperian loop to measure solenoid’s magnetic field

Electronic – Can a solenoid have its magnetic field “focused”

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