Meaning of potential with respect to Earth

[EddiePhys]

Potential of a body is defined as the amount of work done in bringing that body from infinity up to some point divided by its charge.

The Earth has zero net charge, so the work done in bringing any charge from infinity till the Earth is zero.

So what do statements like, "The potential of this body wrt Earth is +5V" or "This positively charged body has positive potential and on grounding, the charge flows into the ground to make it's potential zero" mean ?

 

[sophiecentaur]

"The potential of this body wrt Earth is +5V"

That statement implies that the body has been charged by moving opposite charges onto the Earth. Net charge is still zero, as with a Capacitor that's taken out of the components drawer.
Your statement of the definition of Potential could be applied to your charged body question. You would take a charge from infinity and bring it to Earth and then you would take an equal and opposite charge and bring it to the body. The difference would be 'the PD' of the body relative to the Earth.

 

[jbriggs444]

Potential of a body is defined as the amount of work done in bringing that body from infinity up to some point divided by its charge.

The Earth has zero net charge, so the work done in bringing any charge from infinity till the Earth is zero.

So what do statements like, "The potential of this body wrt Earth is +5V" or "This positively charged body has positive potential and on grounding, the charge flows into the ground to make it's potential zero" mean ?

Potential of a body is defined as the amount of work done in bringing that body from an arbitrary reference point up to the point you are interested in divided by the charge. Taking the reference point to be at infinity is less arbitrary than most choices. This makes infinity a common choice of reference point.

For practical purposes, it is often more convenient to select a less remote reference point. Such as the potential of the chassis on an automobile or the grounding wire on an appliance. When one talks about the potential with respect to Earth, it is this latter choice that is being used. The Earth is selected as the reference point.

If you connect the negative terminal of a 1.5 volt cell to the earth, then a test charge at the positive terminal will have a potential of +1.5V with respect to the earth.

 

[sophiecentaur]

But that is only a simple problem if you have introduced a charge imbalance between the object and the earth. the work done in inductively charging the Earth with a nearby charged object (charges collected elsewhere) is not the same. Induced charge can cause attraction but never repulsion.

 

[EddiePhys]

Potential of a body is defined as the amount of work done in bringing that body from an arbitrary reference point up to the point you are interested in divided by the charge. Taking the reference point to be at infinity is less arbitrary than most choices. This makes infinity a common choice of reference point.

For practical purposes, it is often more convenient to select a less remote reference point. Such as the potential of the chassis on an automobile or the grounding wire on an appliance. When one talks about the potential with respect to Earth, it is this latter choice that is being used. The Earth is selected as the reference point.

If you connect the negative terminal of a 1.5 volt cell to the earth, then a test charge at the positive terminal will have a potential of +1.5V with respect to the earth.

Even if we choose the Earth to be our reference, the electrostatic work done in moving a body from one point to another will be zero unless there is another charged body nearby in which case potential will defined with respect to the position from that charged object.
I don't understand how defining potential with respect to an uncharged body like Earth makes sense

 

[jbriggs444]

Even if we choose the Earth to be our reference, the electrostatic work done in moving a body from one point to another will be zero unless there is another charged body nearby in which case potential will defined with respect to the position from that charged object.

Placing the negative terminal of a 1.5 volt cell in contact with the Earth creates just such a charged object -- the positive terminal.

Edit: On re-reading your response, I see that you feel that the reference point for potential energy is somehow fixed. That is, if you have a charged object here, the reference must be there. This is completely false. The reference point is arbitrary. It is a free choice. If you say "potential with respect to earth", that means that you have chosen the Earth as your reference point.

We are free to choose the reference point because potential itself is physically meaningless. Only potential differences are meaningful.

 

[conscience]

Even if we choose the Earth to be our reference, the electrostatic work done in moving a body from one point to another will be zero unless there is another charged body nearby in which case potential will defined with respect to the position from that charged object.
I don't understand how defining potential with respect to an uncharged body like Earth makes sense

I am not an expert . If I say something incorrect others may correct me .

1) Potential is defined at a point .

2) Potential of a body can only be defined for conductors. Since they are conductors, the electric potential is the same everywhere inside them or on their surface.

Potential of a body(conductor) means potential at any point on it since it is equipotential .

So , when one says that potential of a body is +5V w.r.t Earth , it means +5 Joule of work will be done in moving a unit positive charge from Earth to a point on the body .

The body whose potential is stated to be +5V will most likely be a charged body , so when a unit charge is transported from Earth to a point on the body , work is done against the electric field .This work done is the potential of the body .

@cnh1995 might have some useful insight in this .