# hw01 - reasoning b Calculate the electric field as a...

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172.102 Homework for Week 1 Due Thu 2/4/16 in Class Instructions: Please explain your reasoning in detail. State where the formulas are coming from, and why they are applicable here. (The goal is, after all, so that we can check and possibly correct your way of thinking.) Please write legibly, and draw large and clearly labeled sketches. 1) Consider a finite line of charge with charge per unit length from –L to +L along the x- axis (below). In this problem we want to calculate the electric field at a point on the y- axis (0,y). a) Use symmetry to determine the direction of the electric field at (0,y). Explain your reasoning. b) Extend the calculation from lecture to calculate the field as a function of L and y. c) Take the limit L  and compare the result to the answer for an infinite line. 2) Consider the same rod but find the field at a point on the x-axis, (x,0), with x>L. a) Use symmetry to determine the direction of the electric field at (x,0). Explain your
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Unformatted text preview: reasoning. b) Calculate the electric field as a function of x and L for x>L. c) Reexpress your answer in terms of Q=2 L and consider the case of x>>L. Show that the answer to part (b) approaches that for a point charge. (To do this you will need to combine terms or do a Taylor expansion. For the latter you may find it useful to know that 1 ሺ1 ൅ ߜሻ ൗ ൎ 1 െ ߜ ). 3) An arc of radius R spans an angle between 0 and /2 in the x-y plane. It has a linear charge density ( ) that depends on as ( )= cos 2 where >0. We want to find the field at the origin (x=0=y). a) Sketch ( ) for ߠ ∈ ሾ0, గ ଶ ሿ . b) Before doing any calculations, indicate, roughly, the direction of the field at the origin (relative size of the x and y components of the field). c) Calculate E x . d) Calculate E y . e) What is the magnitude of the field, and what angle does it form with the x-axis? x y R...
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