- #1
RMJ
- 13
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Hello,
There is a common setup used when describing the intimate relationship between electricity and magnetism. I have a question about the setup.
Setup:
There is some long current-carrying wire. Outside of that wire, there is some test charge.
In the first situation, the test charge is stationary.
The wire (carrying non-zero current) is said to be electrically neutral (let's say with average charge velocity Vdrift). In this case the charged particle is said to be subject to no electric or magnetic forces, and thus does not accelerate.
In the second situation, the test charge begins to move with the same speed (and in the same direction, let's say) as the moving charges in the wire.
In the reference frame of the wire, the particle experiences a magnetic force (simply, F=qv x B). In the reference frame of the particle, however, there seems to be an electric force because the charges moving in the current (in the reference frame of the wire/lab) are not moving from the test charge's perspective and the charges not moving in the current (in the reference frame of the wire/lab) are now moving in the opposite direction of the test charge (with average charge velocity of -Vdrift) meaning that the the lengths between them are now contracted (in the reference frame of the particle). When deriving an expression for the coulomb force experienced by this test charge in its own reference frame we might construct an argument saying that the charges that are not moving in the particle's reference frame are more separated than the particles that are moving in the particle's reference frame, and so there is a non-zero linear charge density in the wire which produces an electric field.
My question is this:
In the second situation, we can think about it from the reference frame of the moving test charge and we know that because one kind of charge is stationary and the other kind of charge is moving with average charge velocity -Vdrift. The moving charges undergo length contraction and create a nonzero charge "on" the wire. (The wire is not electrically neutral.)
If we view the FIRST situation from the perspective of the stationary test charge we see that the roles of the charges from the second situation (from the reference frame of the moving test charge) are reversed. There is one kind of charge moving at velocity Vdrift and another kind of charge that is stationary. Why doesn't length contraction occur with the moving charges in this scenario now and create an electric field too (just in the other direction)?
There is a common setup used when describing the intimate relationship between electricity and magnetism. I have a question about the setup.
Setup:
There is some long current-carrying wire. Outside of that wire, there is some test charge.
In the first situation, the test charge is stationary.
The wire (carrying non-zero current) is said to be electrically neutral (let's say with average charge velocity Vdrift). In this case the charged particle is said to be subject to no electric or magnetic forces, and thus does not accelerate.
In the second situation, the test charge begins to move with the same speed (and in the same direction, let's say) as the moving charges in the wire.
In the reference frame of the wire, the particle experiences a magnetic force (simply, F=qv x B). In the reference frame of the particle, however, there seems to be an electric force because the charges moving in the current (in the reference frame of the wire/lab) are not moving from the test charge's perspective and the charges not moving in the current (in the reference frame of the wire/lab) are now moving in the opposite direction of the test charge (with average charge velocity of -Vdrift) meaning that the the lengths between them are now contracted (in the reference frame of the particle). When deriving an expression for the coulomb force experienced by this test charge in its own reference frame we might construct an argument saying that the charges that are not moving in the particle's reference frame are more separated than the particles that are moving in the particle's reference frame, and so there is a non-zero linear charge density in the wire which produces an electric field.
My question is this:
In the second situation, we can think about it from the reference frame of the moving test charge and we know that because one kind of charge is stationary and the other kind of charge is moving with average charge velocity -Vdrift. The moving charges undergo length contraction and create a nonzero charge "on" the wire. (The wire is not electrically neutral.)
If we view the FIRST situation from the perspective of the stationary test charge we see that the roles of the charges from the second situation (from the reference frame of the moving test charge) are reversed. There is one kind of charge moving at velocity Vdrift and another kind of charge that is stationary. Why doesn't length contraction occur with the moving charges in this scenario now and create an electric field too (just in the other direction)?