Electric Potential

You may have noticed that the word "voltage" seems to pop up from time to time….

What does it mean?

 

Question: How can a bird (like this bluebird) stand on a high voltage line without getting zapped?

Answer: Because there is no difference in Voltage across his feet!

Positive Plate (V+)

Negative Plate (V-)

 

A better term for voltage is "Electric Potential difference" .

More precisely:

The electric potential differnce is the difference in potential energy per unit charge

Where U is the potential energy.

Remember How Potential Energy is defined:

Since E and ds are generally in opposite directions, the integral is negative and in this case, the electrical potential difference between the two plates is positve.

In this case…

Its customary to consider the negative terminal (ground) to be at zero potential (Vb= 0)

 

 

 

 

In this case, we would say that

V = (qd/eo)A

at the positive plate, and

V = zero at the negative plate.

Question: instead of knowing q, what if we simply know that the potential difference between the plates is 10 volts.

What is the electric field strength if the plate separation is 1 cm?

A: V = Ed in this case, so E = 10 volts/cm = 1000 N/C

 

Question: How much work would it take to push a one coulomb charge from the negative plate to the positive plate?

 

A: well, voltage is work/charge, so it would take 10 Joules/Coulomb x 1 coulomb equals 10 Joules!

 

Question: If a 10 volt battery "pushes" 5 amps of current through a ciruit, how much power does it "deliver" to the circuit?

 

A: Voltage is Work/coulomb, and the current is 5 coulombs/sec, the the batter delivers 10 Joules/Coulomb x 5 coulombs/s = 50 Joules/s = 50 watts…basically, Power = Voltage x current.

Relation between V and E

…….since

 

 

 

 

 

 

If the Electric field is constant over a small region Dx, then E = -DV/Dx

And the direction is "downhill" just like the gradient in a topograpic map.

 

What is the Electric field strength between the charges shown above?

 

 

 

 

 

Also note that Voltage is a scalar quantity….i.e. there are no vectors involved in the calculations….for example, remember the charges in the previous lecture on the Electric field. In this case, where is the electric potential zero zero?

 

Answer: the voltage is zero at (a). and (c)..

Check out this UC Davis lecture on electric potential….

 

http://maxwell.ucdavis.edu/~electro/potential/overview.html