L03_viet_Electric Field_Field Lines and charge distribution

L03_viet_Electric Field_Field Lines and charge distribution...

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Physics 122 Electricity and Magnetism Lecture 3 Electric Field, Field Lines and Charge Distributions
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05/13/09 Physics 122 - Lecture 3 2 Electric Charge Distributions
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05/13/09 Physics 122 - Lecture 3 3 Electric Field of a Point Charge 2 0 1 ˆ 4 q E r r πε = r Positive Negative
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05/13/09 Physics 122 - Lecture 3 4 Electric Field Superposition on q F E q = r r net 1 on q 2 on q F F F = + + r r r L on q 1 on q 2 on q net 1 2 i i F F F E E E E q q q = = + + = + + = r r r r r r r L L Therefore, the electric field of any charge distribution can be calculated by dividing the distribution into point charges and superimposing these. q
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05/13/09 Physics 122 - Lecture 3 5 The Electric Field of Multiple Point Charges net 1 2 i i ( ) ( ) ( ) ( ) x x x x E E E E = + + = L net 1 2 i i ( ) ( ) ( ) ( ) y y y y E E E E = + + = L net 1 2 i i ( ) ( ) ( ) ( ) z z z z E E E E = + + = L net 1 2 i i E E E E = + + = r r r r L Component electric fields may be superimposed to obtain the net field. This is very useful in calculating the field produced by a number of point charges. This is really three equations:
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05/13/09 Physics 122 - Lecture 3 6 The E-Field of 3 Point Charges in the plane of reflection symmetry net 1 2 3 E E E E = + + r r r r net 1 2 3 ( ) ( ) ( ) ( ) 0 (symmetry) y y y y E E E E = + + = net 1 2 3 1 2 ( ) ( ) ( ) ( ) 2( ) ( ) x x x x x x E E E E E E = + + = + 2 2 2 2 0 2 0 1 1 ( ) (field on x-axis) 4 4 x q q E r x πε = = ( 29 1 1 3/ 2 2 2 2 2 2 2 2 0 1 0 0 1 1 1 ( ) cos 4 4 4 x q q x qx E r x d x d x d θ = = = + + + ( 29 net 3/ 2 2 2 2 0 1 2 ( ) 4 x q x E x x d = + + ( 29 net 3/ 2 2 2 2 0 1 2 ˆ 4 q x E i x x d = + + r q 1 =q 2 3
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05/13/09 Physics 122 - Lecture 3 7 ( 29 net 3/ 2 2 2 2 0 1 2 ( ) 4 x q x E x x d πε = + + ( 29 3/ 2 0 2 2 2 lim 0 x x x d E = + ( 29 3/ 2 2 2 3 2 2 2 1 2 1 2 3 lim ; x d x x x x x x x d + = + = + ?
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L03_viet_Electric Field_Field Lines and charge distribution...

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