# What would be the electric field lines for parallel plates with different charge density?

How would electric field lines look like if charge densities on parallel plates (like the ones used in parallel plate capacitors) are different (still opposite though so electric fields can form)?

• Are you thinking that field line pattern changes? What kind of picture do you have in your mind? – Jack Rod May 2 '20 at 7:19
• What do you think they’d look like (how they would change)? – Bob D May 2 '20 at 7:20
• so if the charge densities of each plate are opposite with equal magnitude, there would be uniform field lines (parallel with equal distance), right? so what would happen if the charge densities are not equal in magnitude? – lina May 2 '20 at 7:54
• @lina The electric field between the plates will still be uniform. Electric forces will cause the charges on each plate to distribute themselves so that when equilibrium is reached the charge density on the inside surfaces of the plates will be equal and opposite creating a uniform field between the plates. The excess charge on each plate will move to the outside surfaces of the plates. The end result is the capacitor will not be overall electrically neutral, as is the case with a normally charged capacitor having equal and opposite charge density.. – Bob D May 2 '20 at 12:49
• The answer is easy to give if one starts with two charges in empty space and add a third. Start with all negative and than make variations with positive, representing the nuclei, which are present in the plates too of course. Anyway the question is nice because complex at a first glance. +1 – HolgerFiedler May 2 '20 at 13:07

## 3 Answers

Electric field lines are a pictorial tool to provide general qualitative information on the nature of the field, specifically the direction and relative strength of the field. The direction is indicated by arrows on the lines. The relative strength in a particular area is indicated by comparing the density of the lines in that area to other areas on the same diagram. The density of the lines provides no quantitative information on the field strength.

Since the strength of the field between the plates of the capacitor is proportional to the charge density, increasing or decreasing the charge density, all other things being equal, would increase or decrease the density of the lines, respectively. However, the density of the lines of a diagram of a single capacitor will tell you nothing because there is nothing to compare it with, such as another capacitor on the same diagram which is identical except for the charge density.

Hope this helps.

I'll drop a hint: Within the same medium, the density of electric field lines is directly proportional to the magnitude of the charge. You can construct your answer from this.

Also, you should try going far back and view the system from infinity.

• This applies to lines of D-field, not E-field. – ProfRob May 2 '20 at 8:00
• @RobJeffries Thanks! I have edited it- Hope it is better – Krishna May 2 '20 at 10:23

As always, the elelectric field lines begin on positive charges, and end on negative charges. Even more precisely: According to Gauss's law the net number of field lines (emerging lines minus entering lines) from a volume element is proportional to the charge enclosed in this volume.

Here is an example with two parallel plates. The positive charge density on the left plate is around 3 times the negative charge density on the right plate. Therefore the number of field lines beginning on the left plate (22) is around 3 times the number of field lines ending on the right plate (7).