Field lines on parallel plates with same charge

[mrcotton]

Homework Statement

Draw the field lines between two parallel plates with +3V on one plate and +1V on the ther

Homework Equations

The Attempt at a Solution

The answer is (D) for a uniform field between the plates, however when two positive charges are drawn the field lines diverge as in (B)
Why is this so, the two situation seem to be very different when all we have done is spread the charge along a line.
Thanks for any help

 

[DimReg]

Field lines can be a little confusing, so it's best to think about what they actually represent. The field lines are supposed to represent the electric field, which by F = qE, tells you how a positively charged particle will be accelerated. (so in A, the positively charged particle repells from the + and goes to the -. In B, it repels from both of them)

So what do you think a positively charged particle would do between the parallel plates?

 

[mrcotton]

Thanks you for the reply,
So in D a positive charge between two parallel plates both with +ve charge and a potential difference. It would try and move towards the lower positive potential bottom plate. What would keep it in a vertical line? If we say it is in the centre of the plates vertically, is it the field either side that keeps it in the vertical? Presumably a positive charge between the plates will further from the +3V plate but never touch the +1 plate?

 

[DimReg]

Microscopically, you have the right idea. When the positive charge gets to the 1V plate, it will repel from the other positive charges on the plate. But it will still find somewhere on the plate it can fit. The other charges will just move around too. However, in order to take these points into account for your drawing, you would have to zoom in very far (to the atomic scale), so that you could draw the individual charged particles.

Have you learned gauss' law yet? You can calculate the electric field fairly easily (if you approx. the plate as infinitely large). If you do that, you'll see that the field lines are perfectly straight.

 

[Nickie]

The reason for the difference in the field lines between the two situations is due to the distribution of charge. In the first situation, where there is a uniform field between the plates, the charge is evenly distributed on the plates. This creates a uniform electric field between the plates, resulting in parallel field lines.

In the second situation, where there are two positive charges on the plates, the charge is not evenly distributed. The charges are concentrated at two points on the plates, creating a non-uniform electric field between the plates. This results in the field lines diverging towards the charges, as they are the source of the electric field.

In both situations, the plates have the same charge, but the distribution of that charge is different, resulting in different field lines. This highlights the importance of considering not just the magnitude of the charge, but also its distribution, when analyzing electric fields.