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# Lecture_03_-_no_quiz_answers - Lecture 3 – 1/18 Electric...

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Unformatted text preview: Lecture 3 – 1/18 Electric Field from Coulomb’s Law • Multiple Point Charges • Continuous Charge Distribution http://www.falstad.com/vector3de/ + – – + + + – P i r – i q i i i i r r q k E ˆ 2 Summation over discrete charges Integral over continuous charge distribution (cylinder with uniform charge) r r dq k E d E ˆ 2 dq P r dV dA dL dq (line charge) (surface charge) (volume charge) Lecture 3 – 2/18 Electric Field from Charged Line (at point P on perpendicular axis) r r dq k E d E ˆ 2 x 1 x 2 sin 2 )] sin( [sin then , If ] sin [sin ) ( cos cos 2 1 1 2 1 1 2 2 2 2 2 2 / 3 2 2 3 2 2 2 1 2 1 2 1 2 1 2 1 y k y k E y k r x r x y k E y x y x y k E y x dx y k r dx y k E r dx k r dq k E y y x x y x x x x y x x x x y 2 2 cos y x r r y dx dq P Lecture 3 – 3/18 Charged Ring • At point P on axis of ring r r dq k E d E ˆ 2 ) 2 ( ) ( ) ( cos 2 / 3 2 2 2 / 3 2 2 3 2 2 a a x x k E ds a x x k E r ds x k E r x r ds k E r dq k E x x x x x R Q L Q 2 Q a x x k E x 2 / 3 2 2 ) ( Lecture 3 – 4/18 Charged Disk • At point P on axis 2 2 2 2 1 2 / 3 2 / 3 2 2 3 2 1 1 2 2 ) ( ) ( 2 cos 2 2 2 2 2 2 x x R x k E u x k E u du x k E dy y x y x k E dq r x k E r dq k E x x R x x x R x x R x x x dr r dA r A 2 2 dy y dq dA dq 2 dy y du x y u 2 so let 2 2 y P 2 1 1 1 2 x R x x k E x Lecture 3...
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Lecture_03_-_no_quiz_answers - Lecture 3 – 1/18 Electric...

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