Does a moving point charge produces an electric field along with magnetic field at a particular point in space and if yes how to calculate it? There is a fixed point in space say (x,y,z) and a point charge 'q' moving with the constant velocity.A magnetic field is produced at (x,y,z) due to moving charge varies as |r|(distance between the 'q' and (x,y,z)) changes.This results in the time-varying magnetic field.And we known time varying magnetic field produced a time-varying electric field.
So, therefore according to this a moving point charge must produce the magnetic field as well as the electric field.
 A: Our knowledge of fields at any point is bound to come from solving the Maxwell equations (either directly or indirectly). We can label some of the special cases with some handy names and remember the solutions to the Maxwell equations for these cases. This information might help us gain some qualitative idea of how the solutions to the Maxwell equations would turn out in some other cases. But in order to actually get the solutions, we have got to solve the equations in their entirety. As you have correctly guessed, a moving charge would produce a varying magnetic field at any point and thus, this variation of magnetic field should also induce some electric field. In order to quantitatively track the electric field produced at any point, you need to solve the Maxwell equations. For a moving charge, the solutions are quite famous and are usually obtained by setting up a Lorenz gauge. The solutions can be intuitively understood in the framework of Lienard-Wiechert potential. Notice that as the Maxwell's equations are already consistent with special relativity, the solutions obtain automatically incorporate the fact that the information of the change in position of a moving charged particle doesn't reach any point faster than light. 
