Ohms law implies specific condition for the charge density

In summary, Ohm's law (J=σE) is a useful approximation for simple electric fields, but it implies conditions on the charge density (ρ) and can result in a reduction of charge density over time in ohmic resistors. This has been observed and is known as the space-charge effect.
  • #1
GarageDweller
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We have all seen Ohms law, J=σE. This approximations makes sense in simple electric fields in which the charges are accelerated in parallel.

However as I will demonstrate, this implies a few conditions on the charge density (ρ) associated with the current density (J).

Now, from the continuity equation, ∂ρ/∂t=-DivJ
=-σDivE (using the approximation)
=-σ(ρ/ε) (From maxwells equations)
This is just a simple partial differential equation, solving...
ρ=A(x,y,z)exp(-σt/ε)+B(x,y,z)
This is a partial differential equation, so we have to allow the coefficients and constants as functions of position.

This implies that at time 0 (when the electric field is set up), the charge density is A+b, after some time the charge density reduces to B(x,y,z).
Has this been observed in ohmic resistors?

I find this result quite strange, is this a physical result?
 
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  • #2
Yes, this result has been observed in ohmic resistors. The charge density of an ohmic resistor is indeed reduced over time as a result of the electric field accelerating charges through the resistor, as predicted by Ohm's law. This phenomenon has been experimentally verified and is known as the "space-charge effect".
 

1. What is Ohm's Law?

Ohm's Law is a fundamental principle in physics that states the relationship between voltage, current, and resistance in an electrical circuit. It states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.

2. How does Ohm's Law relate to charge density?

Ohm's Law does not directly relate to charge density. However, it can be used to calculate the current density in a material, which is related to the charge density. The current density is equal to the current divided by the cross-sectional area of the material, and the charge density is equal to the current density multiplied by the charge of the particles in the material.

3. What is the specific condition for charge density in Ohm's Law?

The specific condition for charge density in Ohm's Law is that the material being studied must be a conductor. This means that the material allows the flow of electric charge through it. Insulators, on the other hand, have very low charge densities because they do not allow the flow of charge.

4. How does Ohm's Law apply to different materials?

Ohm's Law applies to all conductive materials, including metals, semiconductors, and electrolytes. However, the resistance of these materials may vary, which will affect the current and voltage in the circuit. Some materials, like metals, have low resistance and therefore follow Ohm's Law closely, while other materials, like semiconductors, have more complex relationships between current and voltage.

5. Can Ohm's Law be used to calculate the charge density in a given material?

No, Ohm's Law cannot be used to directly calculate the charge density in a material. However, it can be used to determine the current density, which is related to the charge density. The charge density can then be calculated by multiplying the current density by the charge of the particles in the material. Other factors, such as the material's resistivity, must also be taken into account when calculating the charge density in a material.

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