Chapt. 23 The Electric Field 183 Full-Answer Problems 023 qfull 00240 2 5 0 moderate thinking: charge rod, integration 1. There is a thin uniformly charged rod of length L . The total charge is q . The rod’s thickness is negligible: it can be treated as a line of charge. a) What is the formula for the electric ±eld a distance x away from one end of the rod and along the axis of the rod? HINTS: Find the expression for charge per unit length and then divide and conquer by integration. Draw a diagram. b) What is the far-±eld limit (but not in±nite-distance limit) approximation to the formula for part (a). 023 qfull 00250 3 3 0 tough math: in±nite line charge 2. What is the electric ±eld (size and direction) around an in±nite line of charge with linear charge density λ . HINTS: Divide and conquer: what is the electric ±eld at an arbitrary point in space due to an arbitrary di²erential bit of the line? Also: by symmetry what must be the direction of the electric ±eld? And lastly, a conversion to angular integration saves nine (of what? cat
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