Question

Let us imagine a charge q in space. At each point in space,there is an electric fieldvector associated with it. Now we start m oving the charge in a direction. We know that electromagnetic influences travel at the speed of light c and hence fields far away couldn't undergo any change in electric field vector. Here is where I am facing a bit problem.

According to coulombs law,the electric field is given by kq/r.² So,at each point in time,the electric field with vary with the distance r
from the source charge will vary both in magnitude and direction. So electric field at each point in space will change in direction and magnitude with the varying position of the source charge. So,is there any error with coulombs law since we know fields far away can't be affected due to electromagnetic influences but coulombs law doesn't seem to take that into consideration and it suggests that fields will keep changing no matter how far the points are?

Answer 1

The electric field at distant points will eventually change, but with a time delay due to electromagnetic influences propagating at the speed of light.

Step-by-step explanation:

The electric field at each point in space will indeed change in direction and magnitude with the varying position of the source charge. This is not an error with Coulomb's law, but rather a consequence of the fact that electromagnetic influences travel at the speed of light. While the fields far away cannot undergo immediate changes, they will eventually experience the influence of the moving charge as the information of its new position propagates at the speed of light. Therefore, the electric field at distant points will eventually change, but with a time delay.