ch22-p032 - 32 We assume q > 0 Using the notation = q/L we...

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32. We assume q > 0. Using the notation λ = q / L we note that the (infinitesimal) charge on an element dx of the rod contains charge dq = λ dx . By symmetry, we conclude that all horizontal field components (due to the dq ’s) cancel and we need only sum (integrate) the vertical components. Symmetry also allows us to integrate these contributions over only half the rod (0 x L /2) and then simply double the result. In that regard we note that sin θ = R / r where 22 rx R =+ . (a) Using Eq. 22-3 (with the 2 and sin θ factors just discussed) the magnitude is () () 22 22 2 22 00 00 /2 2 32 22 2 0 22 00 0 22 2 2 00 2 2s i n 44 22 21 22 4 2 LL L L dq dx y E rx R x R qLR Rd x x Rx R xR qL q LR R LR LR θ πε πε πε πε πε πε
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This note was uploaded on 06/07/2010 for the course PHYS 344 taught by Professor Bb during the Spring '10 term at The Petroleum Institute.

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