Why does there have to be an electric field if there is a potential difference?
Why does there have to be an electric field if there is a potential difference?
Start by noting that the electrical potential is an energy per unit charge.
In an electric field E the field produces a force on a charge Q of:
F = EQ so if we move the charge a distance dr the work done is just force times distance or:
W = EQ dr The work done per unit charge is Edr, and this is what we mean by the change in the potential:
dV = E dr (1) Now, you start by saying you understand why there must be a potential when there is an electric field, and obviously it's because if there is a field then there is a force on a charge, and there must be an associated energy change given by equation (1) when we move that charge. We get the energy change, i.e. the potential difference, by integrating equation (1):
ΔV = ∫ E.dr (2) But we can rearrange equation (1) to give:
E = dV / dr (3) This is telling us that if there is an energy change dV when we move a unit charge a distance dr then there must have been some force acting on the charge to do that amount of work. This force is the field E times the (unit) charge, so the conclusion is that if the potential changes with distance there has to be a field E present.
Start by noting that the electrical potential is an energy per unit charge.
In an electric field E the field produces a force on a charge Q of:
F = EQso if we move the charge a distance dr the work done is just force times distance or:
W = EQ drThe work done per unit charge is Edr, and this is what we mean by the change in the potential:
dV = E dr (1)Now, you start by saying you understand why there must be a potential when there is an electric field, and obviously it's because if there is a field then there is a force on a charge, and there must be an associated energy change given by equation (1) when we move that charge. We get the energy change, i.e. the potential difference, by integrating equation (1):
ΔV = ∫ E.dr (2)But we can rearrange equation (1) to give:
E = dV / dr (3)This is telling us that if there is an energy change dV when we move a unit charge a distance dr then there must have been some force acting on the charge to do that amount of work. This force is the field E times the (unit) charge, so the conclusion is that if the potential changes with distance there has to be a field E present.
