# I have a constant velocity point charge, do I need to measure it's electric field as if it's moving even if I look at it at a snapshot moment?

I have a point charge and a Gaussian sphere in a spherical coordinate system. The Gaussian sphere is centered at the origin. I need to verify the integral form of Gauss' law for a Gaussian sphere centered at the origin at the moment my point charge moving in the $$\hat z$$ direction with constant velocity $$\vec v$$ is also at the origin. I know that the electric field for a moving charge is different than a stationary one, however I don't see how this is relevant if I look at a snapshot of the point charge when it's at the origin along with the Gaussian sphere. The problem doesn't state it but I'm assuming that I'm not in the same reference frame as the charge.

Wouldn't the electric field at that specific moment in time be the same as it would be for a stationary charge? Or is the fact that it's moving before and after that moment change it's electric field no matter what time I look at it?

HOWEVER, it is important to point out that you haven't mentioned whether the velocity in this case is relativistic. If not (i.e. $$v \ll c$$), then the electric field of the moving charge will look identical to that of a stationary charge because, e.g.: $$E_y' = \frac{E_y}{\sqrt{1-(v/c)^2}}=E_y,$$ and $$E_x' = \frac{E_x}{\sqrt{1-(v/c)^2}}=E_x,$$ since $$(v/c)^2$$ will be very close to $$0$$.