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# Electric potential and Electric Field

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1. How can the electric potential in the exact center of two equal but opposite charges be zero, but the electric field be non zero?
2. (Original post by SirRaza97)
How can the electric potential in the exact center of two equal but opposite charges be zero, but the electric field be non zero?
Two explanations here (the less mathematical one):

Potential is a scalar quantity while field is a vector quantity. Therefore, for the potential you just add the values (so if there is a positive and a negative charge, it will be zero in the centre) whereas for the field the direction must also be taken into account.

Explanation 2 (the slightly more mathsy but slightly simplified version - the derivatives are technically partial derivatives so be careful):

so it is the rate of change of the potential that is important for the field strength.
3. (Original post by SirRaza97)
How can the electric potential in the exact center of two equal but opposite charges be zero, but the electric field be non zero?
Potential is a measure of energy per unit charge, and energy is always scalar is how I think of it, but the electric field can deflect a positively charged particle in opposite directions despite them having equal magnitude
4. (Original post by SirRaza97)
How can the electric potential in the exact center of two equal but opposite charges be zero, but the electric field be non zero?
The potential at point A tells you how much work you have to do to move a +ve unit charge from infinity to that point. It takes no work to move such a charge to the central point between two charges, since, overall, it is as equally attracted to the -ve charge as it is repelled from the +ve charge when being moved to that point i.e. overall, it feels no nett force.

The electric field at point A tells you in which direction a +ve unit charge feels a force. So at the centre point, such a charge feels a non-zero force along the line joining the centres of the charges, from the +ve to the -ve charge. The strength of the force is the rate of change with displacement of the potential at that point.

So the potential is zero at that point but its rate of change in space is not. More mathematically, consider the graph of in the range . At the point , but the slope of the graph i.e. its rate of change with displacement is not 0, rather it is 1 (everywhere).
5. (Original post by atsruser)
The potential at point A tells you how much work you have to do to move a +ve unit charge from infinity to that point. It takes no work to move such a charge to the central point between two charges, since, overall, it is as equally attracted to the -ve charge as it is repelled from the +ve charge when being moved to that point i.e. overall, it feels no nett force.

The electric field at point A tells you in which direction a +ve unit charge feels a force. So at the centre point, such a charge feels a non-zero force along the line joining the centres of the charges, from the +ve to the -ve charge. The strength of the force is the rate of change with displacement of the potential at that point.

So the potential is zero at that point but its rate of change in space is not. More mathematically, consider the graph of in the range . At the point , but the slope of the graph i.e. its rate of change with displacement is not 0, rather it is 1 (everywhere).
That makes a lot of sense thank. Is the electric field between two euqally charged particles at the centre zero? Is the potential zero as well?
6. (Original post by SirRaza97)
That makes a lot of sense thank. Is the electric field between two euqally charged particles at the centre zero? Is the potential zero as well?
Isn't this the question that I've just answered?
7. (Original post by atsruser)
Isn't this the question that I've just answered?
8. (Original post by SirRaza97)
How can the electric potential in the exact center of two equal but opposite charges be zero, but the electric field be non zero?
Say the positive charge is on the left, and the negative charge is on the right, and then you put a positive charge right in the middle. You would have to put in energy in order to push the charge to the left, whereas the charge would move to the left and gain kinetic energy if you left it to its own devices.

Think of it like a ball halfway up a hill: pushing the ball up the hill would increase its potential energy, whereas letting it roll down the hill would decrease its potential energy.

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