# Electric Potential midway between a pair of equal opposite charges

Hi
I need help to understand how electric potential could be zero at the center of two equal but opposite charges. It seems, there is a no field free region anywhere inside the space between the charges. If I move a test charge from negative to positive charge or otherwise, there seems to be no point where I will not have to do work or field won't do work, so how could the potential be zero. I saw this example in a book. Mathematically it sounds good but I could not figure it out intuitively.
I have read in another book, while searching it, that electric potential at the centre of a charged ring is not zero, although electric field is zero there. It has further put me in confusion that potential is non zero at a place where there is no electric field. That is very counter intuitive. I d be thankful for the replies.
High regards.

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Doc Al
Mentor
I need help to understand how electric potential could be zero at the center of two equal but opposite charges.
Realize that the reference point for 0 potential is infinitely far from both charges. So when you move to a point equidistant from both charges, you do positive work against one charge's field but negative work against the others (since they have opposite charge). So the net work done is zero.

It has further put me in confusion that potential is non zero at a place where there is no electric field.
In a region where the field is zero, there can be no change in potential (since you do no work against the field). But that doesn't mean the potential itself is zero.

Realize that the reference point for 0 potential is infinitely far from both charges. So when you move to a point equidistant from both charges, you do positive work against one charge's field but negative work against the others (since they have opposite charge). So the net work done is zero.
Thanks Doc Al for your valuable time.
Is there anyway to explain it when we move the test charge from negative source charge to the positive one. In this case we have to keep pushing the charge all along the path and hence do work. How could the potential be zero midway then?

Doc Al
Mentor
Is there anyway to explain it when we move the test charge from negative source charge to the positive one.
Ask yourself: What's the potential at the location of one of the charges? Is it even defined? (Remember that the 0 point is at infinity.)

In this case we have to keep pushing the charge all along the path and hence do work.
Sure you do work in moving the test charge from near one charge (not exactly at it) to the midpoint, so the change in potential is not zero. But the starting potential is not zero.

Note that when they say that the potential is zero midway between the charges it means that no net work is done in moving a test charge from infinity to that point.

I'd be happy if some learned friend relate this to gravitational field. I have studied one example of an object moving along an elevation in the gravitational field and potential is said to be zero at the ground level. I could not completely understood it.

Sure you do work in moving the test charge from near one charge (not exactly at it) to the midpoint, so the change in potential is not zero. But the starting potential is not zero.

Note that when they say that the potential is zero midway between the charges it means that no net work is done in moving a test charge from infinity to that point.
Thanks Sir.
Here I share my confusions. I feel that when we say there is zero potential at a point, it means a test charge will will experience no force there and will stand still. It will have no potential energy stored in it. Please correct me where I am wrong.

jbriggs444
Homework Helper
potential is said to be zero at the ground level
The zero point in a potential field is arbitrary. For ordinary practical purposes with gravity on earth, it is common to put the zero point at local ground level and pretend that the gravitational field is constant. For gravity over distances where the inverse square law is important, it is common to pout the zero point at infinity.

Neither choice matters greatly since absolute potential is unimportant. Only potential differences are physically meaningful. However, when doing homework and answering questions on tests, it is important to understand what zero point the author is assuming.

Note that when they say that the potential is zero midway between the charges it means that no net work is done in moving a test charge from infinity to that point.
Yes this solves the problem if taken this way. But moving along the line joining the charges, even if coming from infinity is still not well understood. I say if a test charge is brought from infinity while moving along the line joining the two charges, how will have zero potential at mid point. Say first it comes to negative charge from infinity and after crossing negative charge, it moves towards positive charge and reaches the mid point. How is net work done per unit charge zero in this situation?
Sorry if I am two too naive in my concepts.
High regards,

jbriggs444
Homework Helper
The work done over a valid path in a potential field is independent of path. It only depends on the end points. That turns out to be part of the definition of a "potential field". The work done over a path that actually passes through the negative charge, however, is undefined since the electric field is infinite at that point. Any path that skirts the negative charge by any finite amount will turn out to have the same work done as any other, however.

Doc Al
Mentor
I feel that when we say there is zero potential at a point, it means a test charge will will experience no force there and will stand still.
Do not confuse potential with field. As jbriggs444 points out, potential is arbitrary (it depends on what you take as your reference point). What matters is potential difference between two points.
It will have no potential energy stored in it.
Midway between those charges the potential (from infinity) is zero, but the potential difference between the midway point and some point closer to one of the charges is not zero at all! Release a positive test charge at that point and it will move toward the negative charge.

Chestermiller
Mentor
Yes this solves the problem if taken this way. But moving along the line joining the charges, even if coming from infinity is still not well understood. I say if a test charge is brought from infinity while moving along the line joining the two charges, how will have zero potential at mid point. Say first it comes to negative charge from infinity and after crossing negative charge, it moves towards positive charge and reaches the mid point. How is net work done per unit charge zero in this situation?
Sorry if I am two too naive in my concepts.
High regards,
Why don’t you do the calculation if you follow this path, and see what you get?

Thanks all scholars.
I got the point. I appreciate your efforts and the spirit to help.
High regards
Zahid Iftikhar