Question

What is electrical potential energy?
what is potential difference?
Thanks for any help!!

Answer 1

is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system.

Answer 2

It starts to help understanding things from Coulomb's Law:

\[F = kq_1q_2/r^2\]

...where k is Coulomb's constant. In looking at this equation, we can see that the Force between two charges. If one charge is accelerated by another charge (let's say charge 2 is accelerated by charge 1), then we understand that work is done.



A slight simplification that helps understanding is to think of potential energy as work that hasn't happened yet.. so we can think of the potential energy as all the work hasn't happened yet up to a radius r:

\[Fr = kq_1q_2/r\]
\[P_E = kq_1q_2/r\]

Notice that because we multiplied the force by a distance, the units of Pe are in joules.

However, this work will depend on the total charge of q2... assuming q1 is the source of the electric field that is causing q2 to be repelled. Assuming we want to know the total amount of work GIVEN the charge that is moving as a result of the field:

\[P_E/q_2 = kq_1/r\]

Note that by our definition:

\[V = P_E/q_2\]

So that if we know the TOTAL amount of moving charge, we can determine the amount of WORK being done per unit charge.

For example, if V= 5J/C, and 2C of charge are moving, then:

Work = (5J/C)*(2C) = 10J of work...

However, because we know that the electric field gets weaker the farther we move away from q1, we know that the amount of work done by q2 must decrease... therefore voltage must be higher closer to q1 than father away from it... this makes sense given:

\[V = kq_1/r\]

Therefore, you could simply think of the potential difference as the difference in voltage between two points. Ie:

\[V_1-V_2 = kq_1/r_1-kq_1/r_2 = potential\_difference\]

This is an extremely simplified way of viewing it, and certainly isn't the most rigorous or accurate way of describing it, but I find it quite intuitive.

It also explains why voltage has the units its does: Volts = J/C

Answer 3

note that this explanation only works if q2 starts a distance of r=0 from q1...

A more mathematically rigorous and complicated explanation exists as describing voltage as the energy required to move q2 an from infinite distance to proximity "r" from q1... however... that's much more nasty and difficult to explain.

Answer 4

Potential energy could also be described as the amount of work it would take to assemble the charges in the picture below.


If you have an charge and start from infinity, the work you must do to place that charge into the configuration above is electrostatic potential energy.

The amount of work to assemble these charges is fixed.

This is very different from electric potential. Electric potential depends on where you are located, vs. the above which is a fixed number once everything has been assembled.