Electric field halfway between dipole isn't 0?

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MCATPhys
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I was just wondering... say you have a dipole, and you wanted to find the net electric field right in the middle.

The electric field from the electron will be:
E = k(-1.60*10^-19)/r^2


The electric field from the proton will be the same magnitude, but opposite direction. Therefore, the net electric field should be zero right?
 
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Say the dipole is located at the origin and oriented along they y axis. If the electron is at x=-a and the proton at x=a then they both contribute equally to the magnitude of E at the origin as you said, but think about the direction in which the E vector at the origin points due to each particle again. For a positive charge E points away and for a negative charge E points towards right?
 
ohhh - so since they are both in the same direction... they add to a non-zero number...?
 
Correct. They both point in the same direction, that is, in the direction from the proton to electron. So the field there is nonzero.
 
It's very large in between the charges.
If the charges were the same polarity there would be zero field at a point but this isn't a dipole.