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A pair of long, rigid metal rods, each of length $L$ , lie parallel to each other on a perfectly smooth table. Their ends are connected by identical, very light conducting springs of force constant $k$ (Figure 20.79$)$ and negligible unstretched length. If a current $I$ runs through this circuit, the springs will stretch. At what separation will stretch. At remain at rest? Assume that $k$ is large enough so that the separation of the rods will be much less than $L .$

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Hence, the separation at which rods remains at rest is $\left(\sqrt{\frac{\mu_{0} L}{4 \pi k}}\right) I$

Physics 101 Mechanics

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Chapter 20

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Motion Along a Straight Line

Motion in 2d or 3d

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Magnetic Field and Magnetic Forces

Sources of Magnetic field

Electromagnetic Induction

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so we can say that on each wire the force of the spring must be equal to the force of the magnetic field. So if we were to say this, that means that we also have to take note that there are two spring forces on each wire. So this is where we use hooks law. So we can say two hooks law with which equals K Times X would be equal to the force of the spring. Two times the force of a spring would be equal to mu. I squared times l divided by two pi X. Now we should find X so X is going to be equal to mu, not times I squared times l divided by a to pi k times 1/2. So this would be how far you need to stretch the spring such that the magnetic field and the force of the spring cancel out on each wire. And again, this would be mu not the magnetic permeability in a vacuum or the primitive ity of three space times. The current squared times the length divided by two pi times K. Here K is the spring constant. That is the end of the solution. Thank you for watching

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