Question Solved1 Answer undefined The figure(Figure 1) shows a thin rod of length L with total charge Q Part A Find an expression for the electric field Ē at distance z from the end of the rod. Give your answer in component form. Express your answer in terms of the variables Q, L, I, unit vectors i, j, and appropriate constants. vo AEO ? Submit Request Answer Provide Feedback Figure < 1 of 1 + + + + + + + + + + + +
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The charge of rod having length L is Q So Line charge density (lambda)=(Q)/(L) consider an element having length dy which is situated at distance if from origin.The charge dq=lambda dyNow the electric field due to une charge element isd vec(E)=(1)/(4piepsilon_(0))(dq)/(r^(2)) hat(r)nere vec(r)=x hat(i)-y hat(j)hat(r)=(x( hat(i))-y( hat(j)))/(sqrt(x^(2)+y^(2)))So d vec(E)=(1)/(4piepsilon_(0))(lambda dy)/(x^(2)+y^(2))(x( hat(i))-y( hat(j)))/(sqrt(x^(2)+y^(2)))=>d vec(E)=(1)/(4piepsilon_(0))(lambda dy)/((x^(2)+y^(2))^(3//2))(x hat(i)-y hat(j))So the total electric field due to rod is{:[ vec(E)=int_(0)^(L)(1)/(4piepsi_(0))(lambda dy)/((x^(2)+y^(2))//2)(x hat(i)-y hat(j))],[=> vec(E)=(1)/(4piepsilon_(0))int_(0)^(L)lambda[(xdy( hat(i)))/((x^(2)+y^(2))^(3//2))-(ydy( hat(j)))/((x^(2)+y^(2))^(3//2))]],[" Here put "g=x tan theta],[dy=xsec^(2)theta ... See the full answer