ch22_p27 - 27. (a) The linear charge density is the charge...

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27. (a) The linear charge density is the charge per unit length of rod. Since the charge is uniformly distributed on the rod, 15 14 4.23 10 C 5.19 10 C/m. 0.0815 m q L λ −− × == = × . (b) We position the x axis along the rod with the origin at the left end of the rod, as shown in the diagram. Let dx be an infinitesimal length of rod at x . The charge in this segment is dq dx . The charge dq may be considered to be a point charge. The electric field it produces at point P has only an x component and this component is given by dE dx Lax x = +− 1 4 0 2 π ε λ b g . The total electric field produced at P by the whole rod is the integral () 2 0 0 00 0 11 1 44 4 , L L x dx E a La Lq aL a εε λλ λ §· = ¨¸ ππ + π + ©¹ λ1 π+ ³ upon substituting qL −= . With q = 4.23 × 10 15 C, L =0.0815 m and a = 0.120 m, we obtain
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ch22_p27 - 27. (a) The linear charge density is the charge...

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