An insulating rod of length 15.7-cm and charge 17 nC is in a plane with a long s

Question

An insulating rod of length 15.7-cm and charge 17 nC is in a plane with a long straight uniform line charge. The linear charge density of the long line charge is 2.7 10-7 C/m. What is the electric force on the rod if the end closest to the line charge is 2.0 cm away? Hint: the electric field from an infinitely long straight uniform line charge is E(r) = 2 k ? /r .

I need for someone to explain and SET UP the integral. Anything more than that is welcome, so I know I understand it, but not necessary.

Explanation / Answer

charge on insulating wire distribute uniformly hence

dq/dr=17*e-9/15.7cm=1.08*e-7

so force dF on element of lengt dr is E*dq==>dF=E*dq

dq=1.08*e-7*dr

E=2k/r

so dF= 2k/r*1.08*e-7*dr

dF= 2k/r*1.08*e-7dr limits from 2cm to 2+15.7=17.7cm

=2*1.08*e-7*k*ln(17.7)- 2*1.08*e-7*k*ln(2)

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