Electric field and potential

[yangxx2]

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Hi everyone,
In my TPRH book it says that you can have a situation where the electric field is zero, but the potential is not.
The example they give is: two equal charges of the same sign, +Q and +Q, separated by a distance d.
They said the potential at the point midway between them would be 2k(+Q)/(1/2d), but the electric field would be 0.

Can somebody explain how the field would be 0?

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So I did a quick search online, and saw put that electric field = 0 if the charges have the same sign and magnitude. But I'm having trouble understanding this, and proving it mathematically with the electric field equation: E=kQ/r^2

 

[bambam02]

The electric field is a vector quantity.. the field lines point away from + charges and towards negative charges so you have to add them using your vector rules

Picture: Take right as the positive direction

Q+)-------> <-------(+Q

Electric field's cancel each other out in the center due to the opposite direction of the opposing field lines.

Mathmatically: Total E field in center = -kQ/(r/2)^2+kQ/(r/2)^2


The potential is scalar, so there are no arrows with directions associated with them

 

[yangxx2]

Got it, I forgot that the field lines point away from (+) charges.
Thank you!