# Is force due to electric field instantaneous? If not then why?

Suppose a charge $q$ is experiencing a force due to charge $Q$. Suppose we move the charge $Q$ very slowly (no acceleration) what's the instantaneous impact on the charge $q$? How will the $q$ react?

• The information travels at the speed of light (em waves). – Farcher Jun 1 '18 at 13:35
• No, it can travel at the speed of light. Take light for example, if I signal someone with a laser, I sent him information at the speed of light. So information can travel at the speed of light. – Frotaur Jun 1 '18 at 13:46
• Yes, information cannot travel faster than the speed of light, but it can travel at the speed of light – Frotaur Jun 1 '18 at 13:57
• @ParanBharali The electric force isn't instantaneous. The electric force changes instantaneously with the electric field, as Steeven said, but changes in the electric field propagate at the speed of light, according to Maxwell's equations. Hence, changes in the electric force can't propagate faster than light. – probably_someone Jun 1 '18 at 17:22
• @ParanBharali This misunderstanding stems from the fact that you misread the first comment that you replied to, which stated "The information travels at the speed of light", to which you replied "information cant travel faster than light" (spot the difference). – JBentley Jun 2 '18 at 2:26

No two things in the universe happen "instantaneously", unless they are at exactly the same location, because "instantaneously" would have different meanings for observers moving at different velocities. Maxwell's equations, which describe electromagnetic interactions perfectly for most practical purposes, contain time-dependent terms that describe the propagation of changes in an electromagnetic field. If your Q is moved at all, whether fast or slow, the resulting change in its field at a distance D does not occur until a time t = D/c. That is, the change propagates out from Q at the speed of light. This is an observable fact that, per special relativity, is the same for all observers.

• "No two things in the universe happen "instantaneously" - doesn't this statement contradict quantum entanglement effect? – user168013 Jun 2 '18 at 14:06
• No, it doesn't, because nothing is propagated in entanglement. Entanglement is a very subtle concept related to conservation laws in the context of QM. By analogy: momentum is always conserved, but it's not necessary for two particles whose net momentum is zero to communicate with each other in order to ensure that they have equal and opposite momenta. – S. McGrew Jun 2 '18 at 14:21

If you accelerate Q, then you will create a changing electric field, which creates a changing magnetic field, which create a changing electric field, etc., and the result will be EM waves emanating from Q, and they will travel at c to q, changing the force on q when they arrive.

But if there's no acceleration, there's nothing to react to. SR says that there is no such thing as an object moving in an objective sense; there is some frame of reference in which Q is stationary and the electric field is fixed. q will experience a changing electric force as it moves through different parts of that field, but the field itself remain constant, and there is nothing to propagate.

It is not instantaneous.According to Lienard Wiechert potential, where one can see that the effect of the charge does not travel faster than light.So force doesn't acts instantly.

• Reasoning in terms of potentials is subtle. In the Coulomb gauge, the effect in the potential really is instantaneous. It is better to argue in terms of the EM field directly (cf. Jefimenko). – AccidentalFourierTransform Jun 1 '18 at 18:45
• @AccidentalFourierTransform the Coulomb gauge is "non-relativistic", so of course, by definition, everything in there is instantaneous. Your statement is correct but not because of the gauge transformations, just because in the universe there are fields and that's it. – gented Jun 2 '18 at 10:59

Suppose you consider q to be at rest. If Q is moving, then the electric force felt by q will point to the delayed position of Q.

If Q is moving uniformly in a straight line, the actual acceleration felt by q, by strain gauges arranged around it, will point in a different position — to the instantaneous position of Q in your reference frame!

At least, that will be the equilibrium state some time after Q starts moving at a steady pace.

This is due to magnetic effects of the moving charge. At least, that is how you interpret the full 4-dimentional majesty of the electromagnetic force from an inertial reference frame.

How do you measure just the pure electric force? A measuring device might be a small dipole pointer. But that is made using charges on one or both ends, which feel the same secondary effects. Off hand, I think the “true” pure-electric charge cannot be measured locally, since the interpretation of the correction effects depends on your reference frame.

But if you start with stationary charges, and monitor everything when Q starts to move, change direction, and other experiments; you can see the initial delay of any effect and work out the rules consistent with the finite speed of propagation.

You can treat that as an instant if you are working with small enough distances and velocities, but it's not. If you'll ever study field theory you'll meet retarded potentials that are just this: the field propagates at the speed of light and it's no longer seen as instant

Electric force is instantaneous in Newtonian physics. In general relativity it is not.

## protected by Qmechanic♦Jun 1 '18 at 19:06

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