The following diagram summarizes some of the key findings from the previous lab investigation.

 

 

To move a positive test charge from a point infinitely far away to a location 300 m from the source charge takes 180 J of work.  Because this work was done against the electric field, the electric potential energy of the system is 180 J at this point.  Note that electric potential energy is defined to be zero at infinity.

 

To move the same positive test charge from a point infinitely far away to a location 100 m from the source charge takes even more work, 539 J to be exact.  The electric potential energy of the system is said to be 539 J at this point.

 

Although this system accurately describes the situation, it is impractical to make these sorts of measurements because measuring the work done moving tiny particles with minute amounts of charge is extremely difficult.  A more practical way to describe these situations is to use a new quantity called  voltage  (or electric potential).

voltage:  the value, in volts, of the change in electric potential energy stored per unit of charge.

 

Voltage is also called electric potential or potential difference.

 

Expressed as an equation:

 

 

Quantity

Symbol

SI Unit

change in electric potential energy

ΔE p

J

charge

q

C

voltage or
electric potential

V

V

 

Note that 1 volt is the electrical potential at a given point in an electric field such that 1 joule of energy is required to move 1 coulomb of charge from infinity to that point.  1 V = 1 J/C

  

The following graphic illustrates how the voltage would be calculated for the results of the previous lab activity:

 

 

The number of volts describes the amount of energy required to move a coulomb from infinity to each location in the field-a value of "90 000 volts" means "90 000 joules per coulomb."

 

 

Self-Check

Answer the following self-check (SC) question then click the "Check your work" bar to assess your responses.

 

SC 9.  

Suppose the test charge shown in the previous diagram was +4.0 mC instead of +2.0 mC.

  1. Explain how this new value for the test charge would affect the amount of work required to move the test from infinity to each location.

  2. Given your answer from SC 9.a., explain how this new value for test charge would affect the value of the voltage at each location.

  3. Does the value of the voltage depend upon the value of the test charge?

   Self-Check Answer

SC 9.

  1. If the charge on the test body were doubled, then it would take twice as much work to move the test body from infinity to each location. Even though the displacement values would remain unchanged, doubling the charge would double the electrostatic force, which would double the amount of work required.

  2. Voltage is the change in electrical potential energy per unit of charge. Doubling the charge also doubles the electrical potential energy stored in the system since the work done on the charge doubles. The overall effect is that the voltage would be unchanged.

  3. No, the value of the voltage is independent of the charge. This is demonstrated in the answer to SC 9.b.