Internal field in a long narrow rod

In summary, the internal field when an axial field of 1 V/m is applied to a long narrow solid rod with an atomic density of 5 \times 10^{28} m^{-3} and a polarizability of 10^{-40} is 0.56 V/m.
  • #1
Mechdude
117
1

Homework Statement


A long narrow solid rod has an atomic density [itex] 5 \times 10^{28}m^{-3} [/itex]
each atom has a polarizability of [itex] 10^{-40} [/itex] . Find the internal field when an axial field of 1 V/m is applied.

Homework Equations


im not sure what formula to use
but here's one:
[tex] p = E_{loc} \sum_{r} n_j \alpha_j [/tex]
may be the claussius-mossoti equation could be useful,
[tex] \sum_{r} N_j \alpha_j = 3 \epsilon_0 \frac{ \varepsilon -1}{ \varepsilon + 2} [/tex]

The Attempt at a Solution


i don't know how to start, i need a clue.

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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  • #2
The polarization of the rod can be calculated using the Clausius-Mossotti equation: p = E_{loc} \sum_{r} n_j \alpha_j where p is the polarization, E_{loc} is the local electric field, n_j is the atomic density, and alpha_j is the polarizability of each atom. Using the values given in the problem statement, we have:p = 1 V/m \times 5 \times 10^{28} \times 10^{-40} p = 5 \times 10^{-12} C/m^2 The internal field is then equal to the polarization divided by the permittivity of free space: E_{int} = \frac{p}{\epsilon_0} E_{int} = \frac{5 \times 10^{-12}}{8.85 \times 10^{-12}} E_{int} = 0.56 V/m
 

What is an internal field in a long narrow rod?

The internal field in a long narrow rod refers to the magnetic field that is present inside the rod itself. This field is generated by the movement of charged particles within the rod and can be measured using a magnetometer.

How does the internal field in a long narrow rod differ from the external field?

The internal field in a long narrow rod is different from the external field in that it is confined within the rod and does not extend beyond its boundaries. The external field, on the other hand, can be measured outside of the rod and may be affected by other external magnetic fields.

What factors affect the strength of the internal field in a long narrow rod?

The strength of the internal field in a long narrow rod is affected by several factors, including the material of the rod, the composition and movement of charged particles within the rod, and the size and shape of the rod itself.

Can the internal field in a long narrow rod be manipulated?

Yes, the internal field in a long narrow rod can be manipulated by using external magnetic fields or by changing the composition and movement of charged particles within the rod. This can be useful in applications such as magnetic storage devices and particle accelerators.

What are some real-world applications of the internal field in a long narrow rod?

The internal field in a long narrow rod has various applications, including in magnetic sensors, magnetic recording devices, and particle accelerators. It is also used in medical imaging techniques such as magnetic resonance imaging (MRI) to produce high-resolution images of the internal structures of the human body.

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