Electric Potential and Charges: Ranking Potential Energies and Potentials, Study notes of Physics

Download Electric Potential and Charges: Ranking Potential Energies and Potentials and more Study notes Physics in PDF only on Docsity!

• Lecture 6.

conversationElectric Potential Energy and Energy

Point charge in uniform field

Dipole in uniform field

The Electric Potential

Review of Last Lecture

protonAfterward, thepotential is 0 V.where therest at point B,released from A proton is

E. remains at rest at B.D. moves toward C with an increasing speed.C. moves toward C with a steady speed.B. moves toward A with an increasing speed. A. moves toward A with a steady speed.

potentialssmallest, thefrom largest to Rank in order,

V a to

V e

A. at the points a to e.

V

d (^) = (^) V e > (^) V c (^) > (^) V a (^) = (^) V b

B.

V

b (^) = (^) V c = (^) V e (^) > (^) V a (^) = (^) V d

C.

V

a

(^) V b (^) = (^) V c (^) = (^) V d (^) = (^) V e

D.

V

a

(^) V b (^) > (^) V c (^) > (^) V d (^) = (^) V e

E.

V

a

(^) V

b (^) =

(^) V

d (^) =

(^) V

e (^) >

(^) V

c

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

The Electric Potential of a Point ChargeThe Electric Potential of a Point Charge

Let

(^) q (^) be the source charge, and let a second charge

(^) q',

(^) a

distance

(^) r (^) away, probe the electric potential of

(^) q.

(^) The

By definition, the electric potential of chargepotential energy of the two point charges is

(^) q (^) is

influence of chargeThe potential extends through all of space, showing the

(^) q , but it weakens with distance as 1/

r .

This expression for

V

(^) assumes that we have chosen

V

(^) = 0 to

be at

(^) r (^) = (^)

.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

The Electric Potential of Many ChargesThe Electric Potential of Many Charges

The electric potential

V

(^) at a point in space is the sum of the

where potentials due to each charge:

(^) r i is the distance from charge

(^) q i to the point in space

In other words,where the potential is being calculated.

(^) the electric potential, like the electric

field, obeys the principle of linear superposition.

Potential by a dipole

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Problem-Solving Strategy: The electric potentialProblem-Solving Strategy: The electric potential

of a continuous distribution of chargeof a continuous distribution of charge

Draw the charge distribution and the point P.

Set up a coordinate system, such that the calculation is as simple as possible

Divide the charge distrbution into small pieces, each carrying charge

(^)
Q.

Write down the field dV, due to dQ at P, using Coulomb’s Law.

dQ in terms of x, y, z, (or (r,Express all distances and angles in terms of coordinates x, y, z; also express

(^)  ) ) as well as dx, dy, etc. Now you have dQ as

function of coordinates and dx, dy, etc.

charge distribution.Summing up dV due to all pieces, you get the total field created by the whole

 ranform the sum into integral.

Calculate the integral.

Potential by a Charged Ring

Everything looks like a point far away…