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Unformatted text preview: 1 January 16, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 1 Physics 132 Introductory Physics: Electricity and Magnetism Winter Quarter 2008 Lecture 6 January 16, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 2 Calculating the Electric Field: Step-by-step 1) Make a good sketch, define your variables, and label the quantities you’ll need in the calculation. Choose a way to divide the charge distribution into small elements, and what variable to use to describe the elements. (e.g. x and dx, or ϕ and d ϕ ) 2) Write down the (a) charge per element dq and (b) the distance to the ‘field point’ r for each element in the distribution. 3) (a) Write dE for each element, using the expressions from step 2. Work them out in terms of the variable to be used for the integration. Determine the limits of the integration. (b) Use the geometric information in your diagram to write down the components of dE . You may find you can ignore some for symmetry reasons, or that a special choice of coordinates is useful. 4) Determine the limits of the integration, and integrate the expressions for each component (e.g. dE x ) to get the components of E . 2 January 16, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 3 Charged Ring (Quantitative) x y z dl z r R ϕ θ dE dE z Charge : dq = λ d l d l = Rd ϕ λ = Q 2 π R Distance : r = R 2 + z 2 dE = 1 4 πε dq r 2 = 1 4 πε λ Rd ϕ R 2 + z 2 ( ) dE z = dE cos θ = dE z R 2 + z 2 E = dE z ∫ = z λ R 4 πε R 2 + z 2 ( ) 3 2 d ϕ 2 π ∫ = z 2 πλ R ( ) 4 πε R 2 + z 2 ( ) 3 2 E = zQ 4 πε R 2 + z 2 ( ) 3 2 Limit as R → 0 with Q constant : E = Q 4 πε z 2 (Coulomb's Law for Point Charge) January 16, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 4 Charged Disk (Quantitative) P x y z r R dr E Add up narrow rings of width...
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This note was uploaded on 04/18/2008 for the course PHYS 132 taught by Professor Beatty during the Winter '08 term at Ohio State.
- Winter '08