# Energy of Magnetic field by current in a long bar

• zhanhai
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.

#### zhanhai

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?

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.