# Current without Voltage and Voltage without Current?

At school I've always learned that you can view Current and Voltage like this:

The current is the flow of charge per second and the Voltage is how badly the current 'wants' to flow.

But I'm having some trouble with this view. How can we have a Voltage without a current? There is nothing to 'flow', so how can it be there? Or is it 'latent' voltage, I mean is the voltage just always there and if a current is introduced it flows?

Also, I believe you can't have current without voltage. This to me seems logical from the very definition of current. But if you have a 'charge' without a voltage, doesn't it just stay in 1 place? Can you view it like that? If you introduce a charge in a circuit without a voltage it just doesn't move?

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What flows is not the voltage but the charge, and that flow is called current. Voltage can be without a current, if you have a single charge, that charge induces a voltage in all space, even if it's empty. Voltage, in the most physical way, is a scalar field that determines the potential energy per unit charge at every point in space.

Now, you can't have currents without voltages because if there's a current there's a charge moving, and every charge produces a voltage, but you can have currents without voltage differences in space. For example, if you have a charged sphere, and you make it rotate, the charge will be on the surface and by rotating the sphere you will have a current on the surface, but the voltage is the same in all surface. Also magnetization of materials can induce currents by the same way.

If you introduce a charge in a circuit without a voltage it just doesn't move?

That's true, it won't move, unless you have some changing magnetic field that may introduce "voltage differences" between the same point, making $\nabla\times E\not =0$, although that wouldn't be electrostatic voltage the way you're seeing it.

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The only exception is that superconductors can carry a current without a voltage. –  Jerry Schirmer Jan 22 at 15:33
@JerrySchirmer Really, isn't it that they just have super low resistence? I mean, I know that a very very very low voltage could produce a huge current, but would a superconductor in total absence of voltage difference produce a current? –  MyUserIsThis Jan 22 at 16:25
superconductors can maintain eddy currents flowing in rings with no externally supplied voltage. –  Jerry Schirmer Jan 22 at 17:51
And i should say that they don't match up with ordinary classical expectations about conductors, because superconductivity is a fundamentally quantum mechanical phenomenon. –  Jerry Schirmer Jan 22 at 17:58
"f you have a single charge, that charge induces a voltage in all space" Is that right, though? I thought voltage has to be defined as a difference in two locations, and the idea of a voltage at a point is meaningless. Or are you saying that if you were to sample two points around this point charge you could measure a voltage as the field strength dropped off? –  Chelonian Sep 20 at 0:09