# Choice of reference potential in electrostatics

1. Aug 16, 2013

### Vibhor

1. The problem statement, all variables and given/known data

While solving problems in electrostatics we assign zero of potential to infinity .But we also assign zero to ground as well.

Now there are electrostatics problems where we use both ground and infinity as zero potential .How is that we have two zero potentials within a same problem?

Is there something common in infinity and ground such that we can choose them as zero potential simultaneously ?

Could somebody help me understand this ?

Thanks !!

2. Aug 16, 2013

### ehild

In practice, the ground is made by sticking a metal rod into wet soil. So you can consider the "ground" as a conductor of infinite extent, at the same potential as infinity.

"Infinity" is not always appropriate to choose as zero of the potential. Think of an infinite charged plate.

ehild

3. Aug 16, 2013

### Vibhor

Thank you ehild

When we say "infinity" we consider some very far off place such that force of interaction between charges is zero.How do we think it as an infinite charged plate ?

4. Aug 16, 2013

### ehild

I did not say that infinity is an infinite charged plate. I asked you what is the potential of an infinite charged plate with respect to infinity?

ehild

5. Aug 16, 2013

### Vibhor

I think it is zero .Right?

6. Aug 17, 2013

### Vibhor

Is the potential of infinite charged plate zero with respect to infinity ?

7. Aug 17, 2013

### ehild

No. It can not be defined. In case you have a very big single charged plate, with the same charge per unit area σ everywhere, then the electric field strength is E=σ/(2ε0) at both sides of the plate at distance d from it. At two different distances, d1 and d2, the potential difference is U(d2)-U(d1) = E(d1-d2).

If d1=0 and d2=d, U(0)=Ed+U(d). You can choose U(d) as the zero of the potential. The potential of the plate with respect to the potential at distance d is Ed. If you choose d infinite far, the potential of the plate is infinite.

In the real life, plates of infinite extent do not exist. Very far away from a big charged plate, it looks small, and the electric field approximates that of a point charge, and the potential goes to zero. But close to the plate, the potential changes linearly with the distance from the plate.

ehild

Last edited: Aug 17, 2013
8. Aug 17, 2013

### Vibhor

The work done in bringing a unit positive charge from infinity to infinite extending conductor(i.e ground) should be zero.

Again,if we assign zero potential to infinity and zero potential to infinite extending conductor ,then,the relative potential of the conductor should be zero.

But you say it cannot be defined .
I am unable to understand.

9. Aug 17, 2013

### ehild

I meant the potential of a charged plate of very big (infinite) size. For that, infinite is not an appropriate reference.

When we speak about ground, it is considered at zero potential.

ehild

10. Aug 17, 2013

### Vibhor

Oh!! I am sorry.I misunderstood what you were saying.

Why ? This is the original question .Why ground is considered at same potential as that of infinity?

Is my reasoning in post#8 correct?

11. Aug 17, 2013

### technician

Edit..removed...my misunderstanding

Last edited: Aug 18, 2013
12. Aug 17, 2013

### ehild

First, you can choose the zero of the potential at any place. The potential is defined by an additive constant. For a point charge, it is convenient to choose the potential tending to zero at infinity. In that case, it is kQ/r at distance r.

When ground is involved in a problem you might bring "infinity", the zero of potential, close to the charges. But the electric field becomes different from that when the zero of the potential is far away, at infinity. See picture. In case of the left one, the potential is zero at infinity. For the right one, the potential is zero at the ground and also at infinity.

And there are problems when the potential is not defined with respect to infinity. In case of infinite charged plate or infinite long charged wire.

ehild

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