I have some confusion in definition of electric flux .
I have been told that No. of electric field lines passing through a surface area gives/represents electric flux but if suppose $n$ number of electric field lines of two different electric fields of same magnitude but at different angles to area element cross it then by this definition flux of both through surface should be same which is wrong as we see from formula of flux
Shouldn't it be No. of electric field lines passing normally to the surface area gives/represents electric flux ?
Best Answer
The formal definition of the flux of a vector field $\mathbf E$ through some surface $S$ is given by
$$\iint_S\mathbf E\cdot\text d\mathbf a$$
where $\text d\mathbf a$ is a vector of magnitude equal to the area $\text da$ and direction normal to the surface $S$.
So yes, you do need to consider the direction of the field.
The "number of field lines" description is a conceptual way to understand it, but that is about as far as it goes. As you note, this doesn't take direction into account. Also, you have to define what your "number of field lines" means, as the number of field lines one decides to uses is subjective.