Gauss' Law-Can't we find the Electric Field (In the vector form) from Gauss' Law? Because in most of the problems I have been doing like the case of a Charge in a solid sphere, I can find the Magnitude of Electric Field by Gauss' Law but not the Electric Field. Am I wrong here?
So you are saying that you can find the strength of the electric field but not its direction? In this case the direction is obvious, because it points outward along a radius, no?
yes, it is since the Electric Field of the charged sphere points in radial direction. However my question was how to write it vectorially?
I would just write it as its magnitude times the unit vector in the radial direction (r hat).
If u don't get the vector first, how would u write its unit vector even though I have got the magnitude of it
I think it's a combination of Gauss's law and common sense. Common sense (aka the utilization of spherical symmetry) tells you that the electric field must be radially directed, and that it must be of the same magnitude everywhere on the Gaussian surface. Gauss's law then tells you what that magnitude is. Generally speaking, you can't really use Gauss's law to find the electric field directly. Only in cases of special symmetry, like this one. Remember that the thing appearing in Gauss's law is not the electric field by itself - it's a nasty integral of a particular component of the electric field over a closed surface. It's not like you can rearrange the variables and solve for the electric field, like we do in algebra class.
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