Electric field vector takes into account the field's radial direction?

[annamal]

Does the electric field vector takes into account the field's radial direction? Usually when we calculate the electric field, we use $\vec E = \frac{kq}{r^2}\vec j$, which is a straight line vector of a positive charge q's electric field. This electric field points from a positive charge q to a point P. But I am confused because the electric field of q is also radially outwards pointing towards P, which means it will have a curved line to point P. The electric field vector doesn't seem to account for that and only points in the $\vec j$ direction. See image.

 

[andrewkirk]

the electric field of q is also radially outwards pointing towards P, which means it will have a curved line to point P.

What makes you think that it will have a curved line? If q is the only charge in the system and is positive, all electric field lines point radially away from q and those radial lines are straight, There will be no curved field lines.

 

[annamal]

What makes you think that it will have a curved line? If q is the only charge in the system and is positive, all electric field lines point radially away from q and those radial lines are straight, There will be no curved field lines.

See attached image. See how the electric field lines are curved?

Source: https://www.physicsclassroom.com/cl... never cross,are perpendicular to the surface.

 

[andrewkirk]

That's because there is more than one charge. As I said in my post, if there's only one charge they will not curve.
The formula you used in the OP is either for the case where there's only one charge or where you are only calculating the electric field attributable to the charge q, not the total electric field. The total field will curve if there are multiple charges but the field attributable to any single charge will not. The curvature arises from the interaction of the fields.