# Electric potential and Electric Field

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How can the electric potential in the exact center of two equal but opposite charges be zero, but the electric field be non zero?

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How can the electric potential in the exact center of two equal but opposite charges be zero, but the electric field be non zero?

**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 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.

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**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?

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**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 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).

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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).

**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).

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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?

**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?

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Isn't this the question that I've just answered?

**atsruser**)Isn't this the question that I've just answered?

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**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?

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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