Peoples Physics Book Version-2

13.5. Electric Potential http://www.ck12.org

13.5 Electric Potential

Like gravity, the electric force can do work and has a potential energy associated with it. But like we use fields to
keep track of electromagnetic forces, we useelectric potential, orvoltageto keep track of electric potential energy.
So instead of looking for the potential energy of specific objects, we define it in terms of properties of the space
where the objects are.

Theelectric potential difference, orvoltage difference(often just called voltage) between two points (A and B) in
the presence of an electric field is defined as the work it would take to move apositive test charge of magnitude 1
from the first point to the second against the electric force provided by the field. For any other chargeq, then, the
relationship between potential difference and work will be:

∆VAB=

WAB

q

[4] Electric Potential

Rearranging, we obtain:

︸︷︷︸W

Work

= ∆︸ V︷︷AB ︸

Potential Difference

×︸︷︷︸q

Charge

The potential of electric forces to do work corresponds to electric potential energy:

∆UE,AB=q∆VAB [5] Potential energy change due to voltage change

The energy that the object gains or loses when traveling through a potential difference is supplied (or absorbed) by
the electric field — there is nothing else there. Therefore, it follows thatelectric fields contain energy.

To summarize: just as an electric field denotes force per unit charge, so electric potential differences represent
potential energy differencesper unit charge. A useful mnemonic is to consider a cell phone: the battery has the
potential to do work for you, but it needs a charge! Actually, the analogy there is much more rigorous than it at first
seems; we’ll see why in the chapter on current. Since voltage is a quantity proportional to work it is a scalar, and
can be positive or negative.