sophiecentaur
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cabraham said:I disagree. The author presents his claim that E and B are there with or without a conductor. I agree with him so far. Then he writes the closed path line integral of E*dl, which is voltage, and relates it to B and area. But the integral E*dl, requires a specific path to have a value. It is a closed loop integral.
If the voltage is there in an imaginary closed loop in space, will charges in free space circulate in said loop? I don't think so. If a voltmeter, VM, were to have its probes placed in 2 points in empty space, would it read a non-zero voltage in the presence of a non-zero E field? What do you think?
The author correctly points out that E & B are there even in empty space. He then concludes that emf which is the integral of E*dl, must also be non-zero, which makes me wonder. In a physical conductor immersed in said fields, charges would move. In space they move, but not in a closed loop like they would in a conductor. Lorentz force is there, and the charges in free space do indeed move, but the path changes. The emf due to varying fields is path dependent. Since the path taken by free electrons in space differs from that taken in a conductor, the voltages are not equal.
To say that a voltage exists in free space can be supported by Maxwell et al. But I don't think it is the same value as the case w/ a conductor because electrons would move along a different path, and voltage value is path dependent. A CRT is an example. Two parallel plates have a charge, and an electron beam is projected between the plates. The electrons get attracted towards the positive plate and away from the negative plate.
In free space, at every point between the plates, it is safe to say there is indeed a potential. But the E field here is static. I've already stated that under static conditions, current can exist w/o voltage and vice-versa. This does not negate my earlier statement involving dynamic conditions.
Same problem, but the field between the plates is ac, sinusoidal for example. The sine curve plate voltage results in a sine curve E field. There is indeed a potential in between the plates, sine curve in nature. But the plates carry a current to maintain the sine E field. Free electrons in between the plates move back and forth, which is ac current.
Dynamic conditions, i.e. time-chaning, are different than static. No ac voltage exists w/o ac current. That is my point. In free space there can be a voltage w/o current, but only static, not dynamic.
As far as joules per coulomb goes, the voltage across the car, bumperto bumper, is the joules per coulomb of charge transported from bumper to bumper. If a resistor were connected across the bumpers, large in value so that its own current generates a B field too small to cancel the external B field, then the voltage is equal to the joules of energy per coulombs transported through said resistor.
Is this clear? Do I need further clarification? BR.
Claude
I think it would because there's a field there. A probe (infinite imdedance voltmeter) would register the appropriate voltage for the field strength and its length.
Because they have mass they would not follow any resulting curved field. I think introducing electrons is really a bad idea for this reason. It's only when in a metal (with almost zero speed,) that electrons will follow curved E field lines.
But DC is only the limit of decreasing frequency there can hardly be a step change in what happens when the current is not changing (in any case, there is no such thing as real DC because it was switched on at some time and will be switched off)
A resistor would also have an equal and opposite emf induced in it so no current would flow. I made this point before in a different context.