A point charge, Q1=-7.2uC, is located at the origin. A rod of length L=2.2m is l
ID: 1886154 • Letter: A
Question
A point charge, Q1=-7.2uC, is located at the origin. A rod of length L=2.2m is located along the x-axis with the near side a distance d=0.65m from the origin. A charge Q=2 17uC is uniformly spread over the length of the rod.
A) Intergrate the for from each slice over the length of the rod, and write an expression for the magnitude of the electric force on the charge at the origin. |F|=?
B) Calculate the magnitude of the force |F|, in newtons, the the rod exerts on the point charge at the origin.
Explanation / Answer
A) linear charge density on the rod, lamda = Q/L
= 2.17*10^-6/2.2
= 9.86*10^-7 C/m
consider a small segment dx which has charge dQ on rod at x distance from the origin.
lamda = dQ/dx
==> dQ = lamda*dx
Force exerted by dQ on point charge,
dF = k*Q1*dQ/x^2
= k*Q1*lamda*dx/x^2
total force acting on Q1,
F = integral dF
= integral k*Q1*lamda*dx/x^2 (x = d to x = d + L)
= k*Q1*lamda*(-1/x) (x = d to x = d+L)
= k*Q1*lamda*(1/d - 1/(d+L))
|F| = k*Q1*lamda*(1/d - 1/(d+L))
B) |F| = 9*10^9*7.2*10^-6*9.86*10^-7*(1/0.65 - 1/(0.65 + 2.2) )
= 7.59*10^-2 N
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