Twisted Coil in a Magnetic Field

[Leitmotiv]

The idea is as it follows:

We have an homogeneus magnetic field that was increased from 0 to B_f. It induced a certain current (that accumulated to a charge Q) in a circular coil of radius a and resistivity \rho constant. The question is, what would be the charge Q' when the coil is twisted (not strangled), forming an 8 of radii a₁ and a₂ in terms of Q?

Thanks for your help

 

[Defennder]

I don't see how charges could accumulate on a conducting coil due to an induced current.

 

[Meir Achuz]

The idea is as it follows:

We have an homogeneus magnetic field that was increased from 0 to B_f. It induced a certain current (that accumulated to a charge Q) in a circular coil of radius a and resistivity \rho constant. The question is, what would be the charge Q' when the coil is twisted (not strangled), forming an 8 of radii a₁ and a₂ in terms of Q?

Thanks for your help

The charge accumulated on a capacitor in series would be Q[a_1^2-a_2^2]/a^2.

 

[Leitmotiv]

Nono, I expressed myself terribly. The idea is ALL the charge that circulated due to i is Q, I mean \int i·dt=Q

 

[Defennder]

Hmm it seems that in the latter case you can't just treat the 8-shape as two separate coils. For the current to flow in a particular direction in one of the the half-coil, it has to flow in the opposite circular direction. This complicates things somewhat.

 

[Archosaur]

The charge accumulated on a capacitor in series would be Q[a_1^2-a_2^2]/a^2.

The charge is separated by the capacitor.

Charge has to be conserved.