Rate of decreasing static field - is it measurable?

[lenfromkits]

If a static charge is placed on an object, and that object begins to move through space, a magnetic field will form around the object (relative to a stationary observer).

At the same time, the static field around the object will begin to reduce. The faster the object moves, the stronger the magnetic field will become and the weaker the static force.

How do we measure that rate of the changing static force? Is this rate completely theoretical (I believe it's something like P=E.H.sineo), or has anyone managed to actually measure the static force at high speeds to 'actually' measure this change? Where could I find those results?

Thanks!
:)

 

[collinsmark]

If a static charge is placed on an object, and that object begins to move through space, a magnetic field will form around the object (relative to a stationary observer).

At the same time, the static field around the object will begin to reduce. The faster the object moves, the stronger the magnetic field will become and the weaker the static force.

How do we measure that rate of the changing static force? Is this rate completely theoretical (I believe it's something like P=E.H.sineo), or has anyone managed to actually measure the static force at high speeds to 'actually' measure this change? Where could I find those results?

Thanks!
:)

Actually, I don't that's quite right. The (static) electric field is not a function of velocity.

$$\vec E = \frac{1}{4 \pi \epsilon _0}\frac{q}{r^2} \hat r$$

$$\vec F_E = q\vec E$$

The magnetic field is, on the other hand.

$$\vec B = \frac{\mu _0}{4 \pi}\frac{q (\vec v \times \hat r)}{r^2}$$

$$F_M = q(\vec v \times \vec B)$$

Thus the total force is,

$$\vec F = \vec F_E + \vec F_M$$

$$= q \vec E + q(\vec v \times \vec B)$$

If you calculate the relative strengths between the electric and magnetic force (as a function of v) you get an interesting result. Note that Maxwell's equations tell us that the speed of light in a vacuum is $$c = \frac{1}{\sqrt{\epsilon _0 \mu _0}}$$.

 

[lenfromkits]

Were not E and H multiplied by each other supposed to equal a constant?

 

[collinsmark]

Were not E and H multiplied by each other supposed to equal a constant?

Something like

$$\vec E \cdot \vec H = \vec E' \cdot \vec H'$$

Yeah, but I think that's more to do with the geometry changing when you go from one from one inertial frame to another inertial frame (at a different velocity) due to Lorenz transformations.

Yeah, I think I see what you mean now. But I'll let others comment from here.

 

[PJC01]

I can assure you that the rate of decreasing static field is indeed measurable. The strength of a magnetic field can be measured using instruments such as a magnetometer, which can detect changes in the magnetic field caused by the movement of an object. Similarly, the static field around an object can be measured using an electrostatic voltmeter.

The rate of change of the static field can be calculated using mathematical equations, such as the one you mentioned (P=E.H.sineo). However, these calculations are based on theoretical models and may not accurately reflect the real-world conditions. To obtain more accurate measurements, experiments can be conducted to measure the static field at different speeds and observe the changes in the magnetic field.

There have been numerous studies conducted on the relationship between static and magnetic fields, and you can find the results in scientific journals and publications. A quick search on reputable databases such as Google Scholar or ScienceDirect should provide you with relevant research papers on this topic.

In summary, the rate of decreasing static field is indeed measurable, and there have been numerous studies and experiments conducted to measure this change. I hope this helps answer your question.