Where an electric field is equal due to two charges?

[mirandab17]

Hey there!

I don't understand how this really works. With each region, how is it that the charges carry over...? The answer is the fourth region. I'm just totally lost, please explain to me. :)

 

[PeterO]

Hey there!

I don't understand how this really works. With each region, how is it that the charges carry over...? The answer is the fourth region. I'm just totally lost, please explain to me. :)

The net electric field is to be zero, so the two fields must separately be in opposite directions - and of equal magnitude.

The electric field due to the positive charge is away from the charge, so left in region I, and right in regions II, III and IV.

The electric field due to a negative charge is towards the charge, so right in regions I, II & III, and left in region IV.

Only in regions I and IV are the two field in opposite direction, so we know it is one of them.

The strength of the field, E, drops off with distance - the further you are from the charge, the smaller the field, E.
AND
The larger the charge, the stronger the field, E, for any specific distance.

In region I, you are closer [stronger E] to the larger [stronger E] charge, so the effects of the + charge will always dominate.

In region IV, you are closer [stronger E] to the smaller [weaker E] charge, so there may be a point where the two fields can effectively cancel.