Question Solved1 Answer Problem 23.44 The figure(Figure 1) shows a thin rod of length L with total charge Q. Figure 1 of 1 L + + + + + + + + + + + + P -* x Part A Find an expression for the electric field & at distance x from the end of the rod. Give your answer in component form. Express your answer in terms of the variables Q, L, X, unit vectors î, ġ, and appropriate constants.

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Transcribed Image Text: Problem 23.44 The figure(Figure 1) shows a thin rod of length L with total charge Q. Figure 1 of 1 L + + + + + + + + + + + + P -* x Part A Find an expression for the electric field & at distance x from the end of the rod. Give your answer in component form. Express your answer in terms of the variables Q, L, X, unit vectors î, ġ, and appropriate constants.
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Transcribed Image Text: Problem 23.44 The figure(Figure 1) shows a thin rod of length L with total charge Q. Figure 1 of 1 L + + + + + + + + + + + + P -* x Part A Find an expression for the electric field & at distance x from the end of the rod. Give your answer in component form. Express your answer in terms of the variables Q, L, X, unit vectors î, ġ, and appropriate constants.
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Length of the rod =Lcharge in the rrod =Q:. Linear charge density,lambda=(Q)/(L)Let us consider an elemental charge dQ at a listance y from the boltor of the rod.The x-component of the alectric field is seen frrm - This diagram to be{:[E_(x)=int(kdQ)/(r^(2))cos theta],[=lambda k int(dy)/(r^(2))cos thetaquad[k=(1)/(4pi6_(0))]]:}{:[" From Fig. "tan theta=(y)/(x)=>y=x tan theta],[:.dy=xsec^(2)theta d theta=>(dy)/(r^(2))=(xd theta)/(r^(2)cos^(2)theta)=(d theta)/(x)[:'x^(2)=r^(2)cos^(2)theta]],[:.E_(x)=k lambdaint_(-theta_(1))^(0)(1)/(x)cos theta d theta],[=(k lambda)/(x)int_(theta_(1))^(0)cos theta d theta],[=(k lambda)/(x)sin theta|_(-theta_(1)) ... See the full answer