Is it a wire? Is it a magnet?

In the early 19 th ^\text{th} century, it was discovered that when current is passed through a loop of wire, it behaves as if it were a magnet.

The direction of north and south of the magnet depends on the direction in which the current flows in the wire, clockwise or anticlockwise.

If we take two loops of wire and pass current in the same direction in both wires, then will they attract or repel?

They repel They neither attract nor repel They attract

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4 solutions

Tom Engelsman
Feb 2, 2017

By the above picture, both wire currents are in the same direction. If we apply the Right-Hand Rule (with the thumb pointed in the current's direction), the magnetic field lines of each wire are in the same direction. This is achieved when opposite poles are facing each other. In the case of the above picture, the south pole of the LHS wire faces the north pole of the RHS wire \Rightarrow the wires will attract.

Two straight wires carrying a current in the same direction attract each other similarly two current carrying loop carrying a current in the same sense when placed coaxially they attract each other.

Rohit Gupta - 4 years, 4 months ago
Peter Macgregor
Feb 9, 2017

We can work out an answer from the principle that the magnetic forces arise from electrical forces + special relativity.

We will start with a simpler problem of long straight wires. Model the wires as simply as possible as lines of fixed equally spaced positively charged particles and an equal number of equally spaced negative particles. When there is no current the net line charge density is zero and there are no forces on the wires.

When the current starts the negative particles move with a constant velocity down the line. From the point of view of a positive particle all the other positive particles are stationary, but the electrons are moving. Special relativity tells us that these moving particles will appear squashed up along the direction of motion due to the 'Fitzgerald contraction'. So from the point of view of the positive particles in one of the wires, the line density of the electrons in the other wire has increased. These positive particles thus see a net negative charge in the other wire, and as we know positive and negative charges attract \boxed{\text{attract}} .

The same argument shows that from the electrons' frame of reference there will also be a attractive force, but this time it is due to an increase in the positive charge density in the other wire! We live in a weird and wonderful world!

Since the loops are made up of parallel infinitesimal line segments it is easy to believe that they too will attract each other.

I never knew that there is an angle of special relativity in this problem. Although, I would like to think on these lines but I am only a novice in it. Can you explain more about 'Fitzgerald contraction'?

Rohit Gupta - 4 years, 3 months ago

Hi Rohit

A quick survey of these ideas is

https://en.wikipedia.org/wiki/Length_contraction

If you are prepared to invest more time in thinking these ideas through I recommend the popular lectures by Leonard Susskind at

https://www.youtube.com/watch?v=toGH5BdgRZ4

good luck

Peter Macgregor - 4 years, 3 months ago
Robert DeLisle
May 14, 2017

If the current runs the same way, the orientation of the poles will be the same (and shown to be perpendicular to the plane of the loop), thus north of one faces south of the other, and they attract.

Sarang R
Feb 11, 2017

When the current is flowing in the clock wise direction (w.r.t to the face on which we observe) a south pole is developed at that face. similliarly,when the current is in the anti clock-wise direction,a north pole is created at that face. In this sutuation, two opposite poles are produced by the current loop on the surface through which they interact and hence they attract each other!!!

In general, we may note here that the parallel currents attract each other and the antiparallel currents repel.

Rohit Gupta - 4 years, 3 months ago

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