4/8/11 1 Physics 122

(composed by Steve Reich)

4/14/10 11 Physics 122

Δ12 mv2( ) = F||

netΔr = Fnet iΔr = W net

ii WU =Δ−

4/8/11 13 Physics 122

ΔUE = −FE ⋅ Δr (small step)

ΔUE = − FE ⋅ Δr( )∑ (lots of little steps)

ΔUE = − FE ⋅drstart

finish

∫

General case

Simplest case (one source charge, one test charge)

ΔUE = − FE ⋅drstart

finish

∫ = −kCqQ

r2dr

ri

rf

∫ = −kCqQdr

r2ri

rf

∫ = −kCqQ1

ri

−1

rf

⎛

⎝⎜⎞

⎠⎟

UE (r) =kCqQ

rNOT A VECTOR – JUST A NUMBER

4/8/11 15 Physics 122

Field of force felt by a positive test charge near a positive source.

Electric Field felt by a positive test charge near a positive source.

F =kqQ

r2

E =kQ

r2

4/8/11 17 Physics 122

Field of force felt by a negative test charge near a positive source.

Electric Field felt by a negative test charge near a positive source.

F =kqQ

r2

E =kQ

r2

4/14/10 18 Physics 122

qUV

qFE ==

4/8/11 19 Physics 122

Potential energy of a positive test charge near a positive source.

Electric Potential of a positive test charge near a positive source.

U =kqQ

r

V =kQ

r

4/8/11 20 Physics 122

Potential energy of a positive test charge near a positive source.

Electric Potential of a positive test charge near a positive source.

U =kqQ

r

V =kQ

r

4/14/10 21 Physics 122

Δ( 12 mv2 ) = Fnet ⋅ Δr

= mg ⋅ Δr

= −mg Δh

ΔUgrav = mgΔh

4/14/10 22 Physics 122

ΔU = −FiΔr

F = −ΔU

Δr(stepping in the direction

of the steepest descent)

4/14/10 23 Physics 122

g =

F

mVgrav =

Ugrav

m= gh

Not equal!

4/14/10 24 Physics 122

r

rto∞