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.
More 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