Does a Conical End Affect the Magnetic Field Strength of a Solenoid?

[mkbh_10]

If instead of a disc shaped end I have a conical end , would there be any change in the measured magnetic field strength at the end of the solenoid keeping current, core and number of turns per unit length constant ?

 

[sleepycoffee]

I believe it should affect (increase) the field.. If you imagine some fixed number of field lines, the tapered ends would concentrate the field lines, increasing flux, which should increase magnetic field strength. This effect is used the in design of electromagnets, where the tip of the iron yoke will be tapered to increase magnetic flux.. e.g. from Magnet polepiece design for uniform magnetic force on superparamagnetic beads:

"The core cross-section was 1×1 cm2, tapering down to the polepiece cross-section of 0.2×1 cm2. A tapered transition from core to polepiece concentrated the magnetic flux in the polepiece."

This would be the field inside of the tapered yoke, however.. If you were measuring flux outside of the solenoid, it would be distance dependent and I don't think should have as much of an effect. If you take a look at the pdf below, section 3.1, you can see that tapered leads are typically used in situations where the air gap between the two ends is small (a solenoid wrapped around so that the two ends are close together), and the field lines diverge much less..

http://www.physics.utu.fi/projects/kurssit/UFYS3032/Generating%20magnetic%20fields1.pdf

 

[mkbh_10]

In the diagram , there are two electromagnets which are oppositely facing each other and with opposite polarities there can be enhancement of magnetic field strength. However if I have a single piece with a tapered end what would happen then . As theory says flux is proportional to area , now at the tapered end , flux would be less compared to the disc.