Magnetic force on a charge outside of toroidal coil

[Alex Farraday]

Homework Statement

Turns of wire would around a toroidal core, carrying a sinusoidal alternating current i(t), represent a toroidal coil in my case. My question is, does magnetic force affect a non-moving charge outside of toroidal core and is there a magnetic field outside of toroidal core? What if the charge moves?[/B]

Homework Equations

Just theoretical explanation.[/B]

The Attempt at a Solution

I guess there is no magnetic field outside of the core, thus, no force affecting the charge outside of the core, but, I feel like I'm utterly wrong :(

 

[Hesch]

Homework Statement

Turns of wire would around a toroidal core, carrying a sinusoidal alternating current i(t), represent a toroidal coil in my case. My question is, does magnetic force affect a non-moving charge outside of toroidal core and is there a magnetic field outside of toroidal core? What if the charge moves?[/B]

Homework Equations

Just theoretical explanation.[/B]

The Attempt at a Solution

I guess there is no magnetic field outside of the core, thus, no force affecting the charge outside of the core, but, I feel like I'm utterly wrong :(

Theoretical explanation: If the coil around the toroidal core is perfect (infinite number of turns) there is no magnetic field outside the core and the coil.

Practical explanation: There is a magnetic field because the coil is not perfect (finite number of turns). Assume that the number of turns around the core are reduced to zero, having a conductor along the core (but not around), then imagine a circulation path around this conductor (and the core). Now Amperes law states:

The circulation integral of H⋅ds = N*I.

Therfore there must be a H-field along this path as N*I = I, ( B = μ₀*H ). So as number of turns are reduced, the magnetic field outside the core will become more appearent due to a nonperfect coil. If the number of turns are infinite, no current will pass through this imagined circulation path.