ch25 - Electrostatic Potential and Energy Chapter Outline...

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Unformatted text preview: Electrostatic Potential and Energy Chapter Outline ENGINEERING PHYSICS II PHY 303L •The electrostatic potential •Calculation of the Potential from the Field Chapter 25: Electrostatic Potential and Energy •Potential in Conductors •Calculation of the Field from the Potential Maxim Tsoi •Energy of Systems of Charges Physics Department, The University of Texas at Austin http://www.ph.utexas.edu/~tsoi 303L: Electric Potential (Ch.25) 303L: Electric Potential (Ch.25) Potential difference and electric potential Potential difference and electric potential potential energy of the charge-field system • When a charge is displaced by ds, the work done by the electric field rr rr F ⋅ ds = q0 E ⋅ ds is: • As work is done by the field, the potential energy of the charge-field system is changed by an amount: rr dU = − q0 E ⋅ ds • For a finite displacement of the charge from A to B the change in potential energy is: electric potential • Electric potential is a scalar characteristic of an V= electric field, independent of any charges that may be placed in the field • Potential difference take the value of the electric potential to be zero at some convenient point ∆V ≡ • The work done by an external agent to move an electric charge q through the field at constant velocity is • The SI unit of both electric potential and potential Br r ∆U = − q0 ∫A E ⋅ ds • The electric force is conservative the line integral does not depend on the path taken from A to B 303L: Electric Potential (Ch.25) U q0 Br r ∆U = − ∫A E ⋅ ds q0 W = q∆ V 1 V = 1 J/C difference is volt (V) • Electric field can also be expressed in V/m • Energy can be measured in eV 1 N/C = 1 V/m the energy a charge-field system gains or loses when a charge of magnitude e is moved through a potential difference of 1V 303L: Electric Potential (Ch.25) Potential difference Potential difference in a uniform electric field equipotential surfaces • Potential difference between two points A and B separated by a distance |s|=d (s||E) B VB − V A = ∆V = − ∫ A • Consider a charged particle moving between two points A and B so that s is not parallel to E rr B E ⋅ ds = − ∫ Eds = − Ed A • Electric field lines always point in the direction of decreasing electric potential rBr rr Br r VB − V A = ∆V = − ∫ E ⋅ ds = − E ∫ ds = − E ⋅ s A A • The change in potential energy of the charge-field system is rr ∆U = q0 ∆V = − q0 E ⋅ s • Positive charge and field system looses potential energy when the charge moves in the direction of the field: ∆U = q0 ∆V = − q0 Ed • Negative charge and field system gains potential energy • VB-VA=VC-VA VB=VC • Equipotential surface surface consisting of points having the same electric potential when the charge moves in the direction of the field 303L: Electric Potential (Ch.25) 303L: Electric Potential (Ch.25) 1 Electric Potential and Potential Energy Electric Potential and Potential Energy due to point charges due to two or more point charges • Potential difference between two points A and B is • by applying the superposition principle Br B r r q ˆ VB − V A = − ∫ E ⋅ ds = − ∫ ke 2 r ⋅ ds A A r The total electric potential at some point P due to several point charges is the sum of the potentials due to the individual charges r ˆ or since r ⋅ ds = ds cos θ = dr VB − V A = − k e q ∫ rB rA • With reference choice V=0 at r = ∞, the electric potential created by point charge is: r dr ke q B ke q ke q = − = r2 r rA rB rA V = ke V = ke ∑ i qi ri q r 303L: Electric Potential (Ch.25) 303L: Electric Potential (Ch.25) Electric Potential and Potential Energy Electric Field from Electric Potential due to point charges due to point charges • V1 is the electric potential at a point P due to charge q1 • electric field and electric potential are related via Br r ∆V = − ∫A E ⋅ ds • To bring a second charge q2 from infinity to P without • The potential difference between two points a distance acceleration, an external agent must do the work ds apart is rr dV = − E ⋅ ds W = q 2V1 • This work is transferred to the system and appears as Er = − potential energy U = q2V1 = ke q1q2 r12 or if the electric field has only x component dV dr dV = − E x dx ⇒ Ex = − dV dx • Electric field is a measure of the rate of change • If the system consists of more than two (e.g., three) with position of the electric potential charges: qq qq q q U = ke 1 2 + 1 3 + 2 3 r r13 r23 12 Ex = − Example 2 303L: Electric Potential (Ch.25) dV dx Ey = − dV dy Ez = − dV dz 303L: Electric Potential (Ch.25) Electric Potential Electric Potential due to continuous charge distribution due to a charged conductor • electric potential at some point P due to the charge • Every point on the surface element dq is of a charged conductor in dV = ke dq r equilibrium is at the same electric potential Br r VB − V A = − ∫ E ⋅ ds A • The total potential at point P is V = ke ∫ dq r • The potential is the conductor and equal to • Reference: the electric potential is taken to be zero its value at the surface when point P is infinitely far from charge distribution 303L: Electric Potential (Ch.25) electric constant everywhere inside Examples 3-6 303L: Electric Potential (Ch.25) Example 7 2 SUMMARY Electrostatic Potential and Energy • When a test charge q0 is moved between points A and B in an electric field E, the change in the potential energy of the charge-field system is • The electric potential: V= • The potential difference between points A and B: in a uniform field: Br r ∆U = − q0 ∫A E ⋅ ds U q0 ∆V ≡ ∆V = − Ed • An equipotential surface is one on which all points are at the same electric potential • The potential energy associated with a pair of point U = ke charges: • The negative derivative of the electric potential gives the components of the electric field: • The electric potential due to a continuous charge distribution: Br r ∆U = − ∫A E ⋅ d s q0 Ex = − dV dx q1q2 r12 Ey = − dV dy V = ke ∫ Ez = − dV dz dq r 303L: Electric Potential (Ch.25) 3 ...
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This note was uploaded on 10/20/2009 for the course PHY 59090 taught by Professor Tsoi during the Spring '09 term at University of Texas.

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