Physics 24100 Electricity & Op-cs Lecture 6 – Chapter 23 sec. 1-3
• Definitions from mechanics (Physics 152/172):
How much work does /ℓ poor Sisyphus do? 1% =−23 ∙1ℓ What is the change in the potential energy of the rock? . 1* =−23 ∙1ℓ
• Conservative force: Net work independent of the path.
– Total work done: %&'( = *+ −*- (change in potential energy) Work Done by Electrostatic Force
• An electric field exerts a force on a charge.
8>9 /ℓ 23 7
• If we push it to the left, we do work on the charge: 1% =−23 ∙1ℓ>0 – The charge gains potential energy. • If we release the charge, it accelerates to the right – The charge loses potential energy. – It gains kinetic energy (total energy is conserved). ! Energy conservation: change in kinetic energy of a particle = - change in potential energy of a particle ! change in kinetic energy of a particle = work done by E- field
Potential Energy vs Electric Potential
∆; = ? 1; =−? 7 ∙1ℓ= ; −;! ! ! – This only depends on the electric potential at points < and =… – Electric potential is a property of the field. • Difference in potential energy: ∆* = : ∆; SI units: Joules – This depends on the charge, :… – It is not a property of the field. SI Units
• Units of electric potential: Joules per Coulomb
! Electrostatic force is conservative force
• circulation of electrostatic field is zero
E dl =0 · Z NB: there is inductive E-ﬁeld, for which work over closed path is not 0 (circulation not 0)
Lecture 6-8 Electric Potential Energy and Electric Potential High U (potential energy) positive Low U charge q0 High V (potential) High V negative
charge q0 Low U
Low V High U Low V
Electric field direction Electric field direction qq Ur() k 0 r
Urq () q Vr() 0 k qr0 Properties of the Electric Potential
• The electric field points in the direction of decreasing electric potential. – As Sisyphus’ rock rolls down hill (direction of 23) it loses potential energy. • So far, our definition only referred to changes in potential energy and differences in electric potential. – You can add an arbitrary constant to the electric potential without changing the potential difference. – But it must be the same value at all points in space. • We usually define the electric potential as the potential difference relative to a convenient “reference point”. Calculating Electric Potential
• If the electric potential is a property of the field, how do we calculate it? • The electric potential of a field at a point "3 is the work per unit charge required to move from the reference point, "3#'+, to the point, "3: % $3 =; "3 −; =−? 7 ∙1ℓ : #'+ $3%&'
• Maybe it would be nice to pick "3#'+ so that ;#'+ =0. Lecture 6-12 Potential at P due to a point charge q From ∞
Ur() Vr()= q0 q0 q = k r Electric Potential due to a Point Charge 1 ! , 7 (= $ (̂ + 4/01 ( 1ℓ =−1( (̂ ( (#'+
# ; (−;(#'+ =−? 7 (∙1ℓ #%&' 3 # 9# 3 " " =− 8 : = − 4567 #%&' # 4567 # #%&'
• We can make ; (#'+ = 0 if we let (#'+ → ∞. Electric Field from a Point Charge
• Electric potential: 1 ! ; (= 4/01 ( • Electric field: [; 1 ! 7 =−Z;=− Z(= $ (̂ [( 4/01 ( V(r) versus r for a positive charge at r = 0
V(r) to kq r
r For a point charge V(r 0)
1/31/2016 22 Demos: + + + R + + + + + R + + + + + + + + + V(r) + kQ + kQ V(R) + R R
Gauss’ law says the sphere looks like a point charge outside R.
Lecture 6-13 Electron Volt • V=U/q is measured in volts => 1 V (volt) = 1 J / 1 C JNm⋅ [VEmV] == =[ ]⋅ = POTENTIALCC DIFFERENCES V2 – V1 NV [E] == Cm 111JCV= ⋅ 1eV≡⋅≅ | e | 1 V 1.602 × 10−19 C ⋅ 1 V (electron volt)
• V depends on an arbitrary choice of the reference point. • V is independent of a test charge with which to measure it. Example This enclosure has an electric The walls of this room have an potential of -750 kV. electric potential of zero volts.
Negatively charged H- hydrogen ions are produced in the enclosure.
How much kinetic energy do they have when the leave the room? Lecture 6-1 Electric Potential Energy of a Charge in Electric Field
• Coulomb force is conservative => Work done by the Coulomb
force is path independent. dl
• an associate potential energy Ur () to charge q0 at any point r in space.
dW q0 E d l Work done by E field Potential energy change dU dW q0 E dl of the charge q0
It’s energy! A scalar measured in J (Joules) Lecture 6-2 Electric Potential Energy of a Charge (continued)