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Today in Physics class we learned that a wire with an electric current flowing through it creates a magnetic field. I was wondering why electrical power lines do not repel or attract each other even though they have large amounts of electrical current flowing through them.
Question Date: 2011-05-02
Answer 1:

Electrical power lines can attract and repel each other, but the amount of force involved is very small under most common conditions. You probably know that two currents in the same direction attract each other, and currents in opposite directions repel. The magnitude of this force over a wire of length L (assuming the currents in each wire are equal) is

F= mu*I2*L/(2*pi*d) where:
-mu is the permeability of free space (1.26*10-6 Newtons/Amp2)
-I is the current in the two wires
-L is the length of the wire (meters)
-d is the distance between the wires (meters)
-F is the resulting force in Newtons, which can be converted to pounds of force by multiplying by 0.225.

To take an example typical of a high power kitchen appliance like a water kettle, the current in the two wires going to the outlet in the wall is about 10A, and the distance between them is about 5mm. Over a 1 meter wire length the force is only 0.004 Newtons, which is a bit under onethousandth of a pound, so it's very small!

The currents involved in utility power lines are larger, but also keep in mind that the power company uses a step up transformer so that the power lines are at a much higher voltage than the 110V or 220V that we use inside the house. The power is equal to voltage times current. This means that even though a single wire may power several blocks worth of houses, the current in the wire is less than the total current going into each house. The wires are also much further apart than in the previous example, and the force is largest for wires closer together. There may be a tiny force between the wires of utility power lines, but it's small enough that we can usually ignore it, the utility poles will keep the wire from moving much.

Answer 2:

Good question.
First off, electrical lines are insulated, which may alleviate the effect somewhat. More importantly, though, electrical power lines carry alternating current - the current isn't going in one direction all the time, and therefore neither is the force. Last, and most important of all, while the VOLTAGE in electrical power lines is tremendous, the CURRENT actually ISN'T very large, so there isn't much force to begin with.

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