To login with Google, please enable popups

or

Don’t have an account? Sign up

To signup with Google, please enable popups

or

Sign up with Google or Facebook

or

By signing up I agree to StudyBlue's

Terms of Use and Privacy Policy

Already have an account? Log in

- StudyBlue
- Arizona
- Arizona State University - Tempe
- Engineering Physics
- Engineering Physics 131
- Shumway
- Feb09.pdf

John L.

File Size:
11
U = 1 4 piepsilon1 0 q 1 q 2 r John Shumway Department of Physics and Astronomy Arizona State University • Tempe • Arizona http://physics.asu.edu/shumway john.shumway@asu.edu PHY 131: University Physics II Lecture 7: Electric Potential Energy Young and Freedman, Chapter 23.1 9:00–10:15, Tuesday, February 8, 2010 PSF 173 • Department of Physics 1 john.shumway@asu.edu In this lecture, we make a connection between the electrostatic forces and the work-energy theorem from PHY 121. K i + U i + W ot her = K f + U f We can always put the electric field into the work done by other forces. But, we will see that electric field is a conserved force, so we can describe it with a potential energy U. (Recall that ΔU = U f -U i = -W f , use either potential energy U or work W f to describe the force.) Recall the potential energies from conserved forces we used in PHY 121: U = mg h U = 1 2 kx 2 U = Gm 1 m 2 r Conservative forces are forces for which the work only depends on the change in position, not on the path. 2 john.shumway@asu.edu The work done by a constant electric field on a moving charge is only a function of the change in position of the charge. W = integraldisplay f i F · d r From mechanics, Using F=qE, W = q integraldisplay f i E · d r For a constant electric field in the x direction, W = qE integraldisplay f i ˆx · d r = qE integraldisplay f i dx = qE ∆ X Thus the change in potential energy is just given by the change in x-coordinate, ∆ U = U f − U i = − W = − qE integraldisplay f i dx = − qE ∆ X 3 john.shumway@asu.edu The electrostatic potential energy in a constant electric field is analogous to the gravitational potential energy near the Earth’s surface. U = mg h h =0 ⇒ U =0 E U = q E y y =0 ⇒ U =0 Recall that we can set the zero of potential energy wherever we want. 4 john.shumway@asu.edu The change in electrostatic energy only depends on the change in position, and is independent the path taken. E y =0 ⇒ U =0 U i = q E y i U f = q E y f ∆ U f = qE ∆ y 5 john.shumway@asu.edu Note: the general expression for the potential energy of a charge in an electric field is a dot product. U = − q E · r You can choose the origin (zero of energy) wherever you want. For a field in the +x direction, this becomes U = − q E x For a field in the -z direction, this becomes U = q E z 6 john.shumway@asu.edu By convention, we set the potential energy of two charges to be zero when they are infinitely far away. U ( r )= − W ∞→ r = − integraldisplay r ∞ E · d r prime = integraldisplay ∞ r 1 4 piepsilon1 0 q 1 q 2 r prime 2 dr prime = q 1 q 2 4 piepsilon1 0 integraldisplay ∞ r dr r prime 2 = q 1 q 2 4 piepsilon1 0 bracketleftbigg − 1 r prime bracketrightbigg ∞ r U ( r )= 1 4 piepsilon1 0 q 1 q 2 r Potential energy is a scalar; it is much easier to work with than a vector force! The potential energy is the negative of the work done by the electric field when bringing the two charges together from infinity, 7 john.shumway@asu.edu If we ever want the electrical force, we can just take a derivative (gradient) of the electric potential energy. ∆ U = U f − U i = − integraldisplay f i F · d r The inverse of this relationship is a gradient, F = ∇ U = parenleftbigg ∂ U ∂ x ˆx + ∂ U ∂ y ˆy + ∂ U ∂ z ˆz parenrightbigg Strategy: to find the electrostatic force on a charge, first calculate how the potential energy depends on the charges position, then take a derivative. 8 john.shumway@asu.edu The total electrostatic energy of a set of charges adds. q 1 q 2 q 3 q 4 U = summationdisplay i