Forces and Fields 8

Electric Potential DifferenceOr Voltage

Consider a mass positioned in a gravitational field

A mass above a reference level (ground) possesses gravitational potential energy.

Work must be done against the force of gravity to increase Ep. (Lifting the object further off the ground increases Ep)

Between the two points in the gravitational field above the ground,(2m and 5m) the difference in Ep can be determined.

9.81 (3.00 )

29.4

P

app

Work E

W F d

W N m

J

3.00m

1.0kg19.6pE J

upFgF

2.00m

pE mgh

Consider a charge placed within an electric field

E

eF

upF

pE greater

pE lesser

pE

+ charge

-

-

d

- charge

-

-

E

pE lesser

pE greater

pEd

downF

eF

Electric Potential Energy

pWork E

• moving the – charge away from the positive charge requires work which increases electric potential energy and moving the – charge toward the negative charge also does the same

•Electrical Ep changes when work is done in moving a charge from one point to another within an electric field

To increase Ep between two unlike charges, move them farther apart.

-q1

E

+appliedF

eF

d

Ep lesser Ep greater

+

p pWork Fd E increases E

Low Ep d

+ -

d

+ -

Higher Ep

•To increase electric Ep between two like charges, move them closer together

the ratio of the change in energy (work, potential or kinetic) per unit charge (1.00 C) within an electrical field

+ +

d

+ +

d

Low Ep Higher Ep

Electrical Potential Difference or Voltage (V)

Eg) two oppositely charged plates

Between the two points that a positive charge has moved within the electric field, there exists a voltage

E

uniform

pE

High Ep low Ep

+

+

++

+

+

+

+

-

-

-

-

-

-

-

-

+ +

Electric potential difference or voltage is the change in potential energy per unit charge.

The ratio of E/q is called a volt and is named after Alex Volta who invented the battery

Equation:

/

EV

q

units are in J C which is equivalent to volts

In Joules

In Coulombs

Examples:A 12.0 volt battery supplies 12.0 joules of

energy to move a 1.00 C charge through a circuit.

The voltage of 1.00 V between two points in an electric field means that 1.00 J of energy is needed to move a 1.00 C charge between the two points in the field.

1.001.00

1.00

E JV V

q C

eF

+

+

++

+

+

+

+

-

-

-

-

-

-

-

-

0kE

1.00 V

1.00 1.00e

p

Work F d

J E J

- -

Example:A charge of -2.60 X 10-3uC is moved from a

positive plate to a negative plate by doing 1.17 X 10-5 J of work. What is the potential difference between the plates?

eF

+

+

++

+

+

+

+

-

-

-

-

-

-

-

-

- -

appliedF

5

9

3

1.17 10

2.60 10

4.50 10

EV

q

J

C

V

5

9

1.17 10

2.60 10

W J

q C

V

2nd Equation for VoltageThe potential difference or voltage between two

oppositely charged plates is determined by the magnitude of the uniform electric field, E, and the distance between the plates.

Equation for voltage between oppositely charged plates:

EV

q

Work, Ep or Ek, energy

ee e

FW F d but E and F Eq

q

So W Eqd

EqdSo V

q

VV Ed and E

d

Example:Determine the electric field strength

between 2 oppositely charged plates 25 cm apart to which 120 V is supplied.

+

+

++

+

+

+

+

-

-

-

-

-

-

-

-

V = 120 v

0.25 m

E

120

0.250480 /

V Ed

VE

dV

Em

V m