# Should point at which E field = 0 coincide with V = 0?

A problem I solved asks this:

There is a point charge of 3q at the origin and another charge of -2q at x = 5. At what value of x relative to the origin is the electric field equal to zero?

So:

E = E1 + E2
0 = E1 + E2
E1 = -E2
kQ1/x2 = -kQ2/(5-x)2

Solving for x, the point at which these fields cancel out is x ≈ 2.75.

At the start of this problem I had mistakenly solved for the point at which the electric potential equals zero:

V = V1 + V2
0 = V1 + V2
V1 = -V2
kQ1/x = -kQ2/(5-x)

Solving for x yields a clean x = 3.00.

Are my calculations correct, or should these points coincide? At a point in which the total electric field equals zero, shouldn't the total voltage be zero as well?

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BvU
Homework Helper
hi,
if you look at the relationship between potential and electric field strength (or at the dimensions), you see that E = 0 if ΔV = 0 for a (small) change in position...

David Day
BvU
Homework Helper
One more thing is that V is only established up to a constant. We usually choose that to have V = 0 at infinity, but that is just a convention.

David Day
hilbert2
Gold Member
There's two points on the x-axis where the electric field is zero (if not including the "point" at ##x\rightarrow\pm\infty##), and neither of them is between the charges when ##Q_1## and ##Q_2## are of different sign as in this problem.

David Day
Chandra Prayaga
Ask your self the following question in 1-dimension. If a function of x is zero at a certain value of x, is its slope equal to zero at the same value of x?

David Day
haruspex
Homework Helper
Gold Member
2020 Award
Ask your self the following question in 1-dimension. If a function of x is zero at a certain value of x, is its slope equal to zero at the same value of x?
Just to clarify, the OP's question is why isn't V zero where E is zero, so the directly analogous question in 1D is the reverse of the above: why isn't the value of the function zero where its slope is zero?

Further to the above replies, there is nothing special about a point where V is zero. Potentials are always relative. You can define any point to be at V=0; the potential at any other point is relative to that.
In many electrostatics questions it is common to define the potential at infinity to be zero, but it is only a convention.
As against that, E=0 does have significance.

David Day
Ask your self the following question in 1-dimension. If a function of x is zero at a certain value of x, is its slope equal to zero at the same value of x?
That really flicked a switch in my head. Thanks for that!