Two cylinders A and B of equal capacity are connected to each other via a stop clock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened.
A screw gauge has least count of 0. For which one of the following, Bohr model is not valid? NEET Atoms. A body weighs 72 N on the surface of the earth. So, there can be no magnetic field.
Obviously, the left hand side of Ampere's equation is zero, since there can be no magnetic field. It would have to be spherically symmetric, meaning radial. On the other hand, the right hand side is most definitely not zero, since some of the outward flowing current is going to go through our circle. So the equation must be wrong. Ampere's law was established as the result of large numbers of careful experiments on all kinds of current distributions.
So how could it be that something of the kind we describe above was overlooked? The reason is really similar to why electromagnetic induction was missed for so long. No-one thought about looking at changing fields, all the experiments were done on steady situations. With our ball of charge spreading outward in the jello, there is obviously a changing electric field.
Imagine yourself in the jello near where the charge was injected: at first, you would feel a strong field from the nearby concentrated charge, but as the charge spreads out spherically, some of it going past you, the field will decrease with time.
Maxwell himself gave a more practical example: consider Ampere's law for the usual infinitely long wire carrying a steady current I , but now break the wire at some point and put in two large circular metal plates, a capacitor, maintaining the steady current I in the wire everywhere else, so that charge is simply piling up on one of the plates and draining off the other.
Looking now at the wire some distance away from the plates, the situation appears normal, and if we put the usual circular path around the wire, application of Ampere's law tells us that the magnetic field at distance r , from. Recall, however, that we defined the current threading the path in terms of current punching through a soap film spanning the path, and said this was independent of whether the soap film was flat, bulging out on one side, or whatever.
With a single infinite wire, there was no escape— no contortions of this covering surface could wriggle free of the wire going through it actually, if you distort the surface enough, the wire could penetrate it several times, but you have to count the net flow across the surface, and the new penetrations would come in pairs with the current crossing the surface in opposite directions, so they would cancel.
Once we bring in Maxwell's parallel plate capacitor, however, there is a way to distort the surface so that no current penetrates it at all: we can run it between the plates! The question then arises: can we rescue Ampere's law by adding another term just as the electrostatic version of the third equation was rescued by adding Faraday's induction term?
The answer is of course yes: although there is no current crossing the surface if we put it between the capacitor plates, there is certainly a changing electric field , because the capacitor is charging up as the current I flows in.
Assuming the plates are close together, we can take all the electric field lines from the charge q on one plate to flow across to the other plate, so the total electric flux across the surface between the plates,. Ampere's law can now be written in a way that is correct no matter where we put the surface spanning the path we integrate the magnetic field around:.
Notice that in the case of the wire, either the current in the wire, or the increasing electric field, contribute on the right hand side, depending on whether we have the surface simply cutting through the wire, or positioned between the plates.
Actually, more complicated situations are possible—we could imaging the surface partly between the plates, then cutting through the plates to get out! In this case, we would have to figure out the current actually in the plate to get the right hand side, but the equation would still apply. Maxwell referred to the second term on the right hand side, the changing electric field term, as the "displacement current".
This was an analogy with a dielectric material. If a dielectric material is placed in an electric field, the molecules are distorted, their positive charges moving slightly to the right, say, the negative charges slightly to the left. Now consider what happens to a dielectric in an increasing electric field. The positive charges will be displaced to the right by a continuously increasing distance, so, as long as the electric field is increasing in strength, these charges are moving: there is actually a displacement current.
Meanwhile, the negative charges are moving the other way, but that is a current in the same direction, so adds to the effect of the positive charges' motion.
Maxwell's picture of the vacuum, the aether, was that it too had dielectric properties somehow, so he pictured a similar motion of charge in the vacuum to that we have just described in the dielectric. The picture is wrong, but this is why the changing electric field term is often called the "displacement current", and in Ampere's law generalized is just added to the real current, to give Maxwell's fourth—and final—equation.
Our mental picture here is usually of a few thin wires, maybe twisted in various ways, carrying currents. More generally, thinking of electrolytes, or even of fat wires, we should be envisioning a current density varying from point to point in space. The question then arises as to whether the surface integral we have written on the right hand side above depends on which surface we choose spanning the path.
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