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Lecture10

# Lecture10 - Physics 132 Introductory Physics Electricity...

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1 January 28, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 1 Physics 132 Introductory Physics: Electricity and Magnetism Winter Quarter 2008 Lecture 10 January 28, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 2 The Electric Potential Just like we defined E as the force per unit charge, define the electric potential V(r) as the potential energy per unit charge. V = U q E = F q Δ U = F d s ⇒ Δ V = E d s E and F are vectors. V and U are scalars. V is measured in volts. Moving 1C through 1V potential difference does 1J of work. 1 V = 1 J C = 1 Nm C E x = V x ; E y = V y ; E z = V z Alternate units for E: Volts/meter (same as Newtons/Coulomb)

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2 January 28, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 3 Equipotential Surfaces and the Electric Field Equipotential surfaces are surfaces of constant V . Equipotentials are perpendicular to the field lines. -40V 0V -10V -20V -30V 40V 30V 20V 10V U=qV Positive charges move to lower V when allowed to move freely. Negative charges move to higher V. Both are moving to lower U! January 28, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 4 Electric Potential of a Point Charge The reference point for the electric potential is often placed at infinity. V( )=0 V ( R ) = E d s r = R = E ( r ) dr R = Q 4 πε 0 r 2 dr = − − Q 4 πε 0 r R R = Q 4 πε 0 R V ( r ) = Q 4 πε 0 r +Q r E ds Integrate the E field from infinity to get V(r) for a point charge.
3 January 28, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 5 Plotting Fields and Potentials Given V(x), plot E(x). E x = V x x x V E x 2 Note: V must be continuous E need not be, and often changes discontinuously at surfaces Changing V by a constant leaves E unchanged. January 28, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 6 Potential of an Electric Dipole (on-axis) +q -q d P z What is the potential of a dipole on its axis? V + = q 4 πε 0 z d 2 V = q 4 πε 0 z + d 2 V ( z ) = V + + V = q 4 πε 0 1 z d 2 1 z + d 2 = q 4 πε 0 z + d 2 z d 2 z d 2 z + d 2 = qd 4 πε 0 1 z 2 d 2 4 p 4 πε 0 z 2 for z >> d

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4 January 28, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 7 Potential in the Plane Perpendicular to a Dipole +q -q d P r How much work is required to bring charge from infinity to a point in the plane of a dipole?
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Lecture10 - Physics 132 Introductory Physics Electricity...

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