Chapt. 23The Electric Field183Full-Answer Problems023 qfull 00240 2 5 0 moderate thinking: charge rod, integration1. There is a thin uniformly charged rod of lengthL. The total charge isq. The rod’s thicknessis negligible: it can be treated as a line of charge.a) What is the formula for the electric field a distancexaway from one end of the rod andalong the axis of the rod?HINTS:Find the expression for charge per unit length andthen divide and conquer by integration. Draw a diagram.b) What is the far-field limit (but not infinite-distance limit) approximation to the formulafor part (a).023 qfull 00250 3 3 0 tough math: infinite line charge2. What is the electric field (size and direction) around an infinite line of charge with linear chargedensityλ.HINTS:Divide and conquer: what is the electric field at an arbitrary point in spacedue to an arbitrary differential bit of the line? Also: by symmetry what must be the directionof the electric field? And lastly, a conversion to angular integration saves nine (of what? cat
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