Electric Potential and Electric Potential Energy Serway - Chapter 16

www.archive.org - Physics B Lesson 32: Electric Potential


How do these work?

The Physics of a Defibrillator
During a heart attack, the heart produces a rapid, unregulated pattern of beats (Cardiac Fibrillation).
A fast discharge electrical energy through the heart can often correct this condition.

Electric Potential Energy


ME = KE + PEGrav + PEElastic + PEElectric

Gravitational Potential Energy
Gravitational potential energy increases when masses are brought into less favorable configurations ∆Ug > 0

Ug

Ug0

m

Electric Potential Energy
Electrical potential energy increases when charges are brought into less favorable configurations ∆UE > 0 +

+

-

+

Electric Potential Energy
Electrical potential energy decreases when charges are brought into more favorable configurations. ∆UE < 0 +

-

+

+

Electric Potential Energy +

+

+ ∆UE = ____

+

– ∆UE = ____

-

Work must be done on the charge to increase the electric potential energy.

Work and Change in Potential Energy
The change in in potential energy when objects move around is equal in magnitude but opposite in sign to the work done by the field:

∆U = −W field
The minus sign indicates that, when the field does positive work on an object the object’s energy is increased.

Ug

Ug0

m

Work and Charge
The electric force on the charge is due to the electric field.
Moving the charge will require work and results in a change in electric potential energy.
The work required and therefore the change in electric potential energy depends on the size of the charge, the E field strength, and the distance moved.

+++++++++++++++ A

q

d B --------------------------

Electric Potential Energy
There is a change in the charges potential energy because work was done to get it to move.
Electrical Potential Energy in a Uniform Electric Field

∆U E = −qEd  The negative sign indicates that the ∆ will increase if the charge is negative and decrease if the charge is positive.  Depends on both the location of the charge and size of the charge (akin to GPE which depends on the location of the mass and the size of the mass).

Electric Potential
Imagine moving a point charge in a collection of fixed charges, what might change?  The electric potential energy may change due to the distances between it and the other charges changing.  Electric potential energy is useful but it is more convenient and easier to measure and therefore more common to use electric potential.
Just as the E field is defined by  

 

the electric

potential is defined by the electrical potential energy per unit charge:

 

Electric Potential Difference
It is most useful to look at the potential difference between two points.
Electric Potential Difference  The change in potential energy of a charge, q, moved from point A to point B, divided by charge.

∆U E ∆V = q

AP

∆U E = q∆V

 The unit is the volt (V).  1 V = 1 J/C

Electric Potential Difference
By combing the expressions for ∆ and ∆ we can derive an expression for the potential difference in an uniform electric field.
Electric Potential Difference in an Uniform Electric Field

v ∆V = − Ed

AP

v ∆V E = ∆r

Where,   ∆ and represents the distance across which the electrical potential difference is measured

Potential Difference due to Point Charges
Consider two charges separated by r. PEE at point A due to moving q1 towards it can be expressed as follows: B

U E = q2VA kq1q2 UE = r

A

r

+

PEE q1 VA = =k q2 r

q1

+

q2


Potential Due to a Point Charge (Potential is a scalar!)

q V =k r

AP

1

q V= 4πε 0 r

Example Problem An electric field is parallel to the x-axis. What is its magnitude of the electric field if the potential difference between x =1.0 m and x = 2.5 m is found to be +900 V? Given: x1 = 1.0 m x2 = 2.5 m ∆V = +900 V Unknown:  =?

Equation:

v ∆V E = ∆r

Solution: ∆  2.5  1.5  1.5  ∆ 900    ∆ 1.5    600 /  600 /

Example Problem: 2 Charges A 5.0 µC point charge is at the origin, and a point charge of -2.0 µC is on the x-axis at (3.0, 0) m. If the electric potential is taken to be zero at infinity, find the total electric potential due to these charges at point P, with coordinates (0, 4.0) m.