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Qring r0 q 2 r dr c qring 2 r0 q 2 d q

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Unformatted text preview: ⎛2 ⎞ 2 = kEπ zσ ⎜ − 2 ⎟ 2 z + R0 ⎠ ⎝z 3 z 2 Physics 2B - Summer Session 2 - C. Palmer R0 r August 7, 2013 28 z   The disk has radius, R0, and has total dE ( r ) z x y charge Q.   Now we are ready to write the electric field from each ring. ⎛ ⎞ 1 z kE = Ez = kE 2πσ ⎜ 1 − 2 ⎟ 4πε 0 2 z + R0 ⎠ ⎝ ⎞ σ⎛ z = ⎜1 − 2 ⎟ 2 2ε 0 ⎝ z + R0 ⎠ Physics 2B - Summer Session 2 - C. Palmer z R0 r August 7, 2013 29 z dEz ( r )   As R0∞   Total charge Q∞ x y   σ stays the same value!   The 2nd term in Ez goes to 0! Ez, Disk ⎞ σ⎛ z = ⎜1 − 2 ⎟ 2 2ε 0 ⎝ z + R0 ⎠ → Ez, Plane σ = 2ε 0 Physics 2B - Summer Session 2 - C. Palmer z R0 r August 7, 2013 30   We have seen the electric fields from many different charge distributions now.   The point of these examples is to learn HOW to find electric fields. kE q ˆ EPoint = 2 r r kE EDipole, Lateral ≈ − 3 p r kE EDipole, Above ≈ 2 3 p z kE λ EInfinite Line = 2 d zQ Ez, Ring = kE 2 2 R0 + z ( ) 3 2 Ez, Disk ⎞ σ⎛ z = ⎜1 − 2 ⎟ 2 2ε 0 ⎝ z + R0 ⎠ Ez, Plane σ = 2ε 0 Physics 2B - Summer Session 2 - C. Palmer August 7, 2013 31 Physics Concept Components Learning Outcome Evaluate the forces of charged objects on one another. Charge and its analogy Evaluate value and magnitude of electric to mass fields at arbitrary points in space. Coulomb’s Law and its Evaluate the potential differences analogy to gravity between objects (surfaces and points). Electric Force and Electric Fields Calculate flux with surface integrals. Fields Electric Flux Deduce electric fields using Gauss’s Law. Gauss’s Law Discern between electric potential and Electric Potential electric potential energy Capacitance Compute electric field and potential for Material Properties point charges Compute electric field and potential from charge distributions Physics 2B - Summer Session 2 - C. Palmer August 7, 2013 32   The idea is that you have a surface (real or not) and you want to know how much electric field is going through it.   Flux is just how much of something goes through some space.   You can think of it as a collection of field lines.   This video displays the main features:   http://www.youtube.com/watch?v=_xsN9zDHRcA   In order to deal with the effect of not over-counting the electric field when the area is tilted, we use a dot product.   To count them all up, we use an integral: ΦE = ∫ Surface E ⋅ dA Physics 2B - Summer Session 2 - C. Palmer August 7, 2013 33   The idea is that you have a surface (real or not) and you want to know how much electric field is going through it.   Flux is just how much of something goes through some space.   You can think of it as a collection of field lines. ΦE = ∫ E ⋅ dA Surface Physics 2B - Summer Session 2 - C. Palme...
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This note was uploaded on 09/10/2013 for the course PHYS 2B 2b taught by Professor Hirsch during the Summer '10 term at UCSD.

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