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HW-3-solution - HW-3 1 Find the electric field a distance z...

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HW-3 1. Find the electric field a distance z above the center of circular disk of radius R which carries a uniform surface charge density . What does your formula give in the limit R and z R  . Solution: Obviously the electric field is in the z direction so we only need to calculate the z component of the electric field. For a ring between r and r+dr, its contribution to the z component electric field is 2 / 3 2 2 0 2 2 2 2 0 2 2 0 ) ( 2 ) ( 4 2 cos ) ( 4 z r zrdr z r z z r rdr z r dq dE z   Then the total electric field is 2 / 1 2 2 0 2 2 0 2 2 0 0 2 / 1 2 2 0 2 / 3 2 2 0 0 2 / 3 2 2 0 0 1 1 2 1 2 1 1 2 ) ( 1 2 ) ( 2 ) ( 2 z R z R z z R z z z r z z r rdr z z r zrdr dE E R R R z For R , 0 2 E which is expected because the disk is like an infinite sheet.
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