A uniformly charged rod of length L and total charge Q lies along the x axis as

Question

A uniformly charged rod of length L and total charge Q lies along the x axis as shown in in the figure below. (Use the following as necessary: Q, L, d, and ke.)

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Ex =                          Ey =                          A uniformly charged rod of length L and total charge Q lies along the x axis as shown in in the figure below. (Use the following as necessary: Q, L, d, and ke.) Find the components of the electric field at the point P on the y axis a distance d from the origin. What are the approximate values of the field components when d >> L? Explain why you would expect these results. This answer has not been graded yet.

Explanation / Answer

see the page 2 of this pdf : http://www.phys.uri.edu/~gerhard/PHY204/tsl31.pdf   .. for formulas and figure

Ey = (k? / yp) * (cos ?1 ? cos ?2)

so.. Ey = (ke * (Q/L) / d) * ( cos 90 - cos ( 180 - tan inverse ( d/L ) )
so.. Ey = ke * (Q/L) * cos ( tan inverse ( d/L) ) / d = ke * (Q/L) * L / ( sqrt ( L^2 + d^2 )*d )

so.. Ey = ke *Q / ( sqrt ( L^2 + d^2 )*d )



Ex = (k? / yp) * (sin ?2 ? sin ?1)

so.. Ex = ( ke * (Q/L) / d ) * [ sin ( 180 - tan inverse ( d/L )) - sin 90 ]
Ex = ( ke * (Q/L) / d ) * [sin ( tan inverse ( d/L )) - 1]

Ex = ( ke * (Q/L) / d ) * [ d / sqrt ( L^2 + d^2 ) - 1 ]


b) when d>>L

Ey ~ ke *Q / ( sqrt ( L^2 + d^2 )*d ) = ke *Q / ( d*sqrt ( 1 + (L/d)^2 )*d )
= ke *Q / d^2


Ex = ( ke * (Q/L) / d ) * [ d / sqrt ( L^2 + d^2 ) - 1 ] = 0

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