Question

Stop and hypothesize what the field diagram would look like for two opposite charges. Are there going to be areas where the value is 0? Where would they be if so? Why not, if you think this is the case?

I BELIEVE THE BELOW IDEA I HAVE IS INCORRECT

With two opposite charges there would be no value where the electric field is zero unless there is a distance equal to 0 between them, but that can’t be so based on the formula. You can infinitely test distance toward 0, but not 0 as there would be an error. The electric field can be an extremely small number.

Answer 1

yes, your thinking is incorrect.

For two opposite charges placed at some distance from each other, there will definitely be a point where net electric field will be zero.

First of all, in order for electric field to be cancel, we need to make sure that the electric field due to both charges at a point cancels (means the electric field vector points in opposite direction)

Now, suppose the following configuration

Here, at any point in between the charges, the electric field cannot be zero because electric field vector will point in the same direction, so they will not be able to cancel.

what if we place out point left to the +3q charge, we see that here electric field vector points in opposite direction but still here one problem is there is that +3q will have greater magnitude of field so it won't given zero net field.

so, our only option is to place the point right to the -q charge.

if we place a point at distance x (to the right) from +3q charge then we have

k*3q / x² - kq² / (x-4)²

3/x² = 1/(x-4)²

x² -12x + 24 = 0

so, we will get two points as x = 2.5 and 9.5 cm

so, at 9.5 cm , the electric field will be zero.

This is just an example. I meant to say that yes, there exists a point where field will be zero in case of two opposite charges.