# Discharging a capacitor faster using an external B-field?

If a capacitor is being discharged and the electric field is varying with time producing the displacement currents, wouldn't it be possible to align a time-varying external magnetic field with the magnetic field produced by the displacement currents to increase the discharge rate? Or the vice-versa slow down the discharge rate?

$$B_{Net} = \Delta B_d + \Delta B_{ext} ∴ \uparrow t_d$$
$$B_{Net} = \Delta B_d - \Delta B_{ext} ∴ \downarrow t_d$$

Where,
##t_d##: The discharge time.
##B_{Net}## : The net magnetic field within the separation region.

From Ampere's law it seems plausible:

$$\oint_C {Bd\ell = \mu _0 I_C }$$

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Nik_2213

tech99
Gold Member
The time varying magnetic field can encompass the space between the capacitor plates or the connecting wires with equal effect. It will induce a voltage in series with the circuit by electromagnetic induction, and is equivalent to placing a dynamo in series with the circuit. If the polarity is such as to aid the flow of current, the capacitor will discharge quicker.
The energy supplied by the dynamo will be expended in additional heating of R.

anorlunda
#PP: Slightly tangential but, given many capacitors are 'rolled up' for volumetric efficiency, and air-gapped variable capacitors are usually multi-plate, so the effects of an external magnetic field would cancel, you'll have difficulties applying this tweak.
Kudos for the lateral thinking !!

sophiecentaur
sophiecentaur
Gold Member
2020 Award
Is this a thought experiment or is there a practical aspect to it. Is the aim to discharge the capacitor as fast as possible or is it to pass a high current through the R?
I'm sort of looking for a Switch somewhere in the circuit??
The current through the load R will depend on the voltage across it.

Baluncore