Energy of Magnetic field by current in a long bar

In summary, the energy density is proportional to the square of B, which is proportional to 1/r. As a result, the EM energy as the space integral of the energy density is infinite, suggesting that a current through a very long bar cannot be realized without a return path. However, for a "very long" bar, the divergence is slow enough to allow for a return path to remove the divergence. Without a return path, a current over a finite distance would accumulate charge and stop the current flow.
  • #1
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Obviously, the energy density is proportional to the square of B, which is proportional to 1/r (radius).

Thus, the EM energy as the space integral of the energy density is infinite.

This would suggest that a current through a very long bar cannot be realized. May I understand such a result as that current flowing through a very long bar can not be truly realized without a returning line for forming a loop?
 
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  • #2
There is a huge difference between "very long" and "infinitely long" as the divergence is very slow (logarithmic in distance). For "very long", you still have a return path somewhere which will remove the divergence.

A current over a finite distance without a return path would accumulate charge somewhere which stops the current flow at some point.
 

1. What is the relationship between current and magnetic field energy in a long bar?

The energy of a magnetic field in a long bar is directly proportional to the current passing through it. This means that as the current increases, so does the energy of the magnetic field.

2. How is the energy of a magnetic field by current in a long bar calculated?

The energy of a magnetic field in a long bar can be calculated using the equation U = (1/2)LI2, where L is the inductance of the bar and I is the current passing through it.

3. What factors affect the energy of a magnetic field in a long bar?

The energy of a magnetic field in a long bar is affected by the current passing through it, the length of the bar, and the strength of the magnetic field produced by the current.

4. How does the energy of a magnetic field in a long bar impact its surrounding environment?

The energy of a magnetic field in a long bar can impact its surrounding environment by inducing currents in nearby conductors or affecting the movement of charged particles, such as electrons. It can also create a force on magnetic materials in its vicinity.

5. Can the energy of a magnetic field in a long bar be converted into other forms of energy?

Yes, the energy of a magnetic field in a long bar can be converted into other forms of energy, such as electrical energy. This can be achieved by moving a conductor through the magnetic field, which will induce a current in the conductor.

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