Electric Potential. AP Physics C Montwood High School R. Casao. Electric Potential Energy. When a force acts on a particle that moves from point a to point b, the work W a b done by the force is given by a line integral: dx is a very small distance along the particle’s path.
AP Physics C
Montwood High School
If the only work done on the particle is done by conservative forces, then Kb – Ka = -(Ub – Ua), which can be rewritten as Ka + Ua = Kb + Ub.
Electric Potential Energy in a Uniform Electric Field
The field exerts a downward force F = qo·E on a positive test charge qo.
The electric force on the charge is constant, therefore, the force exerted on qo is conservative.
If a negative charge moves in the direction of the electric field E, the electric field does negative work on the charge and the potential energy U increases.
If q and qo have the same sign, the force F is repulsive and F is positive; if q and qo have opposite signs, the force F is attractive and F is negative.
The work done by the electric force for a particular path depends only on the end points.
If qo returns to its starting point a by any path, the total work done is zero (displacement is zero); integral from ra to ra = .
Left figure: If q and qo have the same sign, the force is repulsive and the work done by the field of q is positive and U is positive at any finite separation.
the total electric field at
each point is the vector
sum of the fields due to
the individual charges, and
the total work done on qo
during any displacement is
the sum of the contributions
of the individual charges.
Work and potential energy are scalar quantities, not vector quantities; keep the negative signs!
When Ua is greater than Ub, the field does positive work on the particle as it “falls” from a point of higher potential energy a to a point of lower potential energy b.
Because the external force is the negative of the electric field force and the displacement is in the opposite direction, the potential difference Ua – Ub is positive.
Potential energy and charge are both scalar quantities, so electric potential is a scalar too..
The difference Va – Vb is called the potential of a with respect to b; sometimes abbreviated as Vab = Va – Vb and called the potential difference between a and b.
Alternative: Vab, potential of a with respect to b, equals the work that must be done to move a unit charge (1 C) slowly from b to a against the electric force.
What Good is the Electric Potential?
Two essential ideas:
If we know the electric potential V throughout a region of space, we know the potential energy U = q·V of any charge that enters the region of space.
Ki + q·Vi = Kf + q·Vf
Calculating the Potential from the Field
For the electric field represented by the field lines in the figure, a positive test charge qo moves along the path shown from point i to point f.
dW = F•ds = qo·E·ds
The potential difference Vf – Vi between any two points i and f in an electric field is equal to the negative of the line integral of E•ds from i to f.
difference in potential between any two points in the electric field.
The loss of electric potential energy is equal to the gain in kinetic energy.
If the test charge is negative, then DU is positive. The test charge gains electric potential energy when it moves in the direction of the electric field.
A unit of energy commonly used in atomic and nuclear physics is the electron-volt. An electron-volt (eV) is the energy that an electron (or proton) gains when moving through a potential difference of 1 V.
1 eV = 1.602 x 10-19 J