P20-030 – How Electric Flux Varies

How Electric Flux Varies

There are three ways that the electric flux can change

1. If the magnitude of the electric field $\overrightarrow{E}$ changes

If the magnitude of $E$ increases, then ${\mathrm{\Phi }}_E$ increases. In general, if $E$ increases, the number of electric field lines increases and therefore the electric flux through a given surface increases.

If the magnitude of $E$ decreases, then ${\mathrm{\Phi }}_E$ decreases. In general, if $E$ decreases, the number of electric field lines decreases and therefore the electric flux through a given surface decreases.

2. If the area $A$ changes

If the area increases, then ${\mathrm{\Phi }}_E$ increases. Indeed, for a given electric field $\overrightarrow{E}$, the greater the area, the greater the number of electric field lines flowing through it and the greater the electric flux.

If it decreases, ${\mathrm{\Phi }}_E$ decreases. Indeed, for a given electric field $\overrightarrow{E}$, the smaller the area, the fewer the number of electric field lines flowing through it and the lesser the electric flux.

3. If the angle $\theta $ changes

As the angle $\theta $ gets closer to $90{}^\circ $, then the number of field lines that cross the surface goes to zero and the flux ${\mathrm{\Phi }}_E$ goes to zero. Indeed, an angle of $90{}^\circ $ corresponds to the electric field lines being parallel to the surface and therefore not crossing it or flowing through it. Conversely, the flux is the greatest when $\theta =0{}^\circ $ because the electric field lines are then perpendicular to the surface and all of the electric field flows through the surface.

In summary you may change the electric flux by changing the magnitude of $E$, the area $A$ through which you are calculating the flux and, finally, the orientation $\theta $ of the surface with respect to the field lines.