Final answer:
The electric field due to stationary charges is conservative, while the field from moving charges is more complex, involving both electric and induced magnetic fields. Gauss's law simplifies static charge situations, but dynamic scenarios require Maxwell's equations. Factoring in the movement of charges and the associated magnetic fields complicates direct application of Newton's laws.
Step-by-step explanation:
The electrostatic field generated by stationary charges is considered conservative, which means the work done in moving a charge from one point to another does not depend on the path taken. This is described by the equation ∣E ⋅ dl =0. The force from a conservative field, like the Coulomb force associated with static electric fields, allows for the definition of potential energy that is only dependent on position. However, the electric field produced by moving charges changes with time and can induce a magnetic field. The problem of calculating forces and fields in such dynamic situations is typically more complex because we have to consider both the electric and magnetic fields, which are part of Maxwell's equations.
Considering moving charges, the electric field is affected by movement and the resulting magnetic fields. Unlike electrostatic fields, magnetic fields are not conservative and cannot be described solely by Coulomb's law. As charges move, the distance and hence the force between them changes, and the direct application of Newtons laws becomes more complicated. Therefore, in dynamic situations like these, physicists rely on techniques such as conservation of energy and Maxwell's equations to describe the behavior of the electric and magnetic fields.
In the case of static charges, Gauss's law provides a much simpler method for determining the electric field for certain symmetrical charge distributions compared to direct integration methods. However, this simplicity is generally not available when dealing with moving charges and their associated magnetic fields, and one has to rely on the complete set of Maxwell's equations to find a solution.