Lecture05 - Physics 132 Introductory Physics Electricity...

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1 January 14, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 1 Physics 132 Introductory Physics: Electricity and Magnetism Winter Quarter 2008 Lecture 5 January 14, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 2 Field Lines of an Electric Dipole Electric dipole: two point charges +q and -q separated by distance d No net charge (neutral), but creates E field anyway Many diatomic molecules act like dipoles (e.g. CO,NO,HCl) Axial symmetry + - + - Two adjacent equal dipoles: “quadrupole”; …
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2 January 14, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 3 Electric Field on the Axis of a Dipole +q -q d E + E - P What is E field at point P? Add fields due to two charges: superposition z r E = r E + + r E E + > E at P r E + = + q 4 πε 0 z d 2 2 ) z r E = q 4 πε 0 z + d 2 2 ) z r E = q 4 πε 0 1 z d 2 2 1 z + d 2 2 ) z = q 4 πε 0 z 2 + zd + d 2 4 z 2 zd + d 2 4 z d 2 2 z + d 2 2 ) z = q 4 πε 0 2 zd z d 2 z + d 2 2 ) z = q 4 πε 0 2 zd z 2 d 2 4 2 ) z January 14, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 4 “Far Field” of an Electric Dipole (on axis) r E = q 4 πε 0 2 zd z 2 d 2 4 2 ) z q 4 πε 0 2 zd z 4 ) z r E qd 2 πε 0 z 3 ) z +q -q d E + E - P z Far away, z >> d. How does E behave? r p = q r d r E = r p 2 πε 0 z 3 Vectors p and d point from - to + charge The combination qd is the dipole moment
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3 January 14, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 5 Continuous Charge Distributions Q Q Q Q λ =Q/L σ =Q/A ρ =Q/V So far: Point Charges Now consider charge Q “smeared out” Line of charge λ : charge per length Surface/sheet of charge σ : charge per area Volume of charge ρ : charge per volume January 14, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 6 Calculating E for a Charge Distribution Charge is really discrete (quantized)… But in real materials there are so many charges we can regard them as continuous.
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