General formula for Electric field of a point charge

In summary, the formula for the electric field for a moving point charge, labelled as (1) on this page, is derived from the Lienerd-Wiechert potentials and Maxwell's equations. It includes a term for the static Coulomb field, the retarded fields due to the finite propagation of light, and radiation caused by acceleration of charges. The third term in the equation is related to the second order time derivative of the retarded position. Understanding this equation may require further study in volume 2 or another resource.
  • #1
elara
1
0
While reading through the Feynman Lectures on Physics (volume 1, number 28) I have come across the formula for the electric field for a moving point charge - it's the equation labelled (1) on this page:

http://maxwellsociety.net/PhysicsCorner/InteractingParticles/AcceleratingCharges.html

Can anyone explain where this comes from?

The first term I recognise as Coulomb's law, but am right in thinking that the second accounts for the time it takes for the change in electric field to propagate to an observer? And then where does the last term come from? Do I need to just take this on faith until I get to volume 2?

Thanks for any help!
 
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  • #2
In general, the fields from a charge are given by the Lienerd-Wiechert potentials. These are derived from Maxwell's equations though it isn't a particularly trivial derivation to do so. But in addition to the static coulomb field, there are the retarded fields due to the finite propagation of light and there is radiation that occurs due to any acceleration of charges. The latter would seem to be the cause of your third term in your referenced equation since it is related to the second order time derivative of the retarded position.
 
  • #3
It's even more complicated than Eq. (1) looks. Taking tlme derivatives of retarded functions is a mess. You definitely have to wait until volume 2, or maybe a better book.
 

Related to General formula for Electric field of a point charge

1. What is the general formula for the electric field of a point charge?

The general formula for the electric field of a point charge is given by E = kq/r^2, where E is the electric field, k is the Coulomb's constant (9x10^9 Nm^2/C^2), q is the magnitude of the point charge, and r is the distance from the point charge to the location where the electric field is being measured.

2. How is the direction of the electric field of a point charge determined?

The direction of the electric field of a point charge is determined by the direction in which a positively charged test particle would move if placed in the electric field. If the test particle is positively charged, it will move away from the point charge, indicating that the electric field is directed outward. If the test particle is negatively charged, it will move towards the point charge, indicating that the electric field is directed inward.

3. Can the electric field of a point charge be zero?

No, the electric field of a point charge cannot be zero. According to the general formula, the electric field is inversely proportional to the square of the distance from the point charge. Therefore, as long as the distance is not zero, the electric field will always have a non-zero value.

4. How does the electric field of a point charge change with distance?

The electric field of a point charge follows an inverse square law relationship with distance. This means that as the distance from the point charge increases, the electric field decreases proportionally. For example, if the distance is doubled, the electric field will decrease by a factor of four.

5. Can the electric field of a point charge be negative?

Yes, the electric field of a point charge can be negative. This occurs when the point charge is negative, as the direction of the electric field will be opposite to the direction of a positive test particle. However, it is important to note that the magnitude of the electric field will still be positive, as it is always calculated using the magnitude of the point charge.

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