Twisted Coil in a Magnetic Field

Main Question or Discussion Point

The idea is as it follows:

We have an homogeneus magnetic field that was increased from 0 to Bf. 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?

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

clem
The idea is as it follows:

We have an homogeneus magnetic field that was increased from 0 to Bf. 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?

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

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
Homework Helper
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.

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.