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You are given a positively charged rod of length L and of univform charge Q. TYhere is a positive test charge qo placed alongside this rod like the figure

+++++++++++++++++++++++++++++++++<-------distance x------>Q

find the net force on Q

First of all there is no y or z component so F refers to the x axis only

One solution :

Let dq = YdL where Y is charge density

then dF = k dq Q/(L+x)^2

dF = kqYdL/(L+x)^2

integrating you get

F = kqY dL/L+x)^2 from 0 to L

then F = kqYL/x(L+x)

then resub for Y = Q /L

F = KqQ/x(x+L)

is there anything wrong with this solutioin please point out a mistake i don't seem to ppick up on.

My prof suggested this way

Divide the rod like so

++++++++++++++++<------distance x--------->Q

<----L/2---><---------(x - L/2)------------------->

then dq = Y dL

dF = k dq Q / (x-L/2)^2

dF = kYdLQ/ (x-L/2)^2

F = kYQ (integrate from 0 to L) dL / (x-L/2)^2

solving gives kqQ/x(2x-L) why this inconsistency of solutions i know one is wrong, but which one??

i have a feeling that the integration for the second one is not done properly...

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# Homework Help: 2 solutions to the same problem but which is the correct one?

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