Vector Potential of Hertzian with Two Positive Charges

Your Name]In summary, the conversation discusses finding the vector potential from two oscillating point charges on the z axis. It is possible to have two positive charges on the z-axis, and the approach to solving this problem is similar to the generic Hertzian problem, with the main difference being in the calculation of the z_+ equation.
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Homework Statement



Find the vector potential from two oscillating point charges on the z axis.

Homework Equations



[itex]z_+ = -z_0cos(\omega t) [/itex]
[itex]q1_+ = q2_+ = q [/itex]

The Attempt at a Solution



I know how to solve this problem when the two charges are equal and opposite, but now the two oscillating charges on the z-axis are both positive. Is this even possible? and if so, how is this different from the generic Hertzian problem? I also question my [itex]z_+[/itex] equation, does this look correct?
 
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Thank you for your question. It is certainly possible to have two oscillating point charges on the z-axis that are both positive. This scenario is different from the generic Hertzian problem because in that case, the two charges are equal and opposite, whereas in this scenario, they are both positive.

To solve this problem, you can use the same approach as you would for the generic Hertzian problem. The main difference will be in the calculation of the z_+ equation. Since both charges are positive, the equation will be z_+ = z_0cos(\omega t), without the negative sign.

I hope this helps. Let me know if you have any further questions.


 

1. What is the vector potential of Hertzian with two positive charges?

The vector potential of Hertzian with two positive charges is a mathematical concept that describes the vector field that arises from the movement of two positive charges in space. It is a measure of the magnetic potential energy at a given point in space, and is often used in electromagnetism and quantum mechanics.

2. How is the vector potential of Hertzian with two positive charges calculated?

The vector potential of Hertzian with two positive charges is calculated using the formula: A = μ0/(4π) * (q1/r1 + q2/r2) where μ0 is the permeability of free space, q1 and q2 are the magnitudes of the two positive charges, and r1 and r2 are the distances from each charge to the point in space where the vector potential is being calculated.

3. What is the significance of the vector potential of Hertzian with two positive charges?

The vector potential of Hertzian with two positive charges is significant because it helps us understand and analyze the behavior of electromagnetic fields. It can help us predict the direction and strength of magnetic forces between charged particles, and is an important concept in the study of electricity and magnetism.

4. How does the vector potential of Hertzian with two positive charges relate to Maxwell's equations?

The vector potential of Hertzian with two positive charges is closely related to Maxwell's equations, which describe the fundamental laws governing electromagnetic fields. In particular, it is related to the equation for the divergence of the magnetic field, as it is a measure of the magnetic potential energy at a given point in space.

5. Can the vector potential of Hertzian with two positive charges be measured experimentally?

Yes, the vector potential of Hertzian with two positive charges can be measured experimentally using various techniques such as magnetic resonance imaging (MRI) and magnetic field sensors. It is an important quantity in many practical applications, including medical imaging, particle accelerators, and magnetic levitation systems.

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