1 / 13

# Physics 2102 Lecture 6 - PowerPoint PPT Presentation

Physics 2102 Jonathan Dowling. Physics 2102 Lecture 6. Electric Potential II. –Q. +Q. U B. Example. Positive and negative charges of equal magnitude Q are held in a circle of radius R. 1. What is the electric potential at the center of each circle? V A = V B = V C =

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Physics 2102 Lecture 6' - skule

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Jonathan Dowling

### Physics 2102 Lecture 6

Electric Potential II

+Q

UB

Example

Positive and negative charges of equal magnitude Q are held in a circle of radius R.

1. What is the electric potential at the center of each circle?

• VA =

• VB =

• VC =

2. Draw an arrow representing the approximate direction of the electric field at the center of each circle.

3. Which system has the highest electricpotential energy?

A

B

C

+Q

-Q

r

Electric Potential of a Dipole (on axis)

What is V at a point at an axial distance r away from the midpoint of a dipole (on side of positive charge)?

Far away, when r >> a:

V

U= QoV=Qo(–Q/d+Q/d)=0

Electric Potential on Perpendicular Bisector of Dipole

You bring a charge of Qo = –3C from infinity to a point P on the perpendicular bisector of a dipole as shown. Is the work that you do:

• Positive?

• Negative?

• Zero?

a

+Q

-Q

P

-3C

• Divide the charge distribution into differential elements

• Write down an expression for potential from a typical element — treat as point charge

• Integrate!

• Simple example: circular rod of radius r, total charge Q; find V at center.

r

dq

dx

a

L

Potential of Continuous Charge Distribution: Example

• Uniformly charged rod

• Total charge Q

• Length L

• What is V at position P shown?

P

Electric Field & Potential: A Simple Relationship!

Focus only on a simple case:

electric field that points along +x axis but whose magnitude varies with x.

Notice the following:

• Point charge:

• E = kQ/r2

• V = kQ/r

• Dipole (far away):

• E ~ kp/r3

• V ~ kp/r2

• E is given by a DERIVATIVE of V!

• Of course!

• Note:

• MINUS sign!

• Units for E -- VOLTS/METER (V/m)

Electric Field & Potential: Example Simple Relationship!

(b)

V

V

(a)

r

r

r=R

r=R

V

(c)

r

r=R

+q

• Hollow metal sphere of radius R has a charge +q

• Which of the following is the electric potential V as a function of distance r from center of sphere?

Electric Field & Potential: Example Simple Relationship!

V

E

• Outside the sphere:

• Replace by point charge!

• Inside the sphere:

• E =0 (Gauss’ Law)

• E = –dV/dr = 0 IFF V=constant

+q

Equipotentials and Conductors Simple Relationship!

• Conducting surfaces are EQUIPOTENTIALs

• At surface of conductor, E is normal to surface

• Hence, no work needed to move a charge from one point on a conductor surface to another

• Equipotentials are normal to E, so they follow the shape of the conductor near the surface.

An uncharged conductor: Simple Relationship!

A uniform electric field:

An uncharged conductor in the initially uniform electric field:

Conductors change the field around them!

“Sharp”conductors Simple Relationship!

• Charge density is higher at conductor surfaces that have small radius of curvature

• E = s/e0 for a conductor, hence STRONGER electric fields at sharply curved surfaces!

• Used for attracting or getting rid of charge:

• lightning rods

• Van de Graaf -- metal brush transfers charge from rubber belt

• Mars pathfinder mission -- tungsten points used to get rid of accumulated charge on rover (electric breakdown on Mars occurs at ~100 V/m)

(NASA)

Summary: Simple Relationship!

• Electric potential: work needed to bring +1C from infinity; units = V

• Electric potential uniquely defined for every point in space -- independent of path!

• Electric potential is a scalar -- add contributions from individual point charges

• We calculated the electric potential produced by a single charge: V=kq/r, and by continuous charge distributions : V= kdq/r

• Electric field and electric potential: E= -dV/dx

• Electric potential energy: work used to build the system, charge by charge. Use W=qV for each charge.

• Conductors: the charges move to make their surface equipotentials.

• Charge density and electric field are higher on sharp points of conductors.