A charge of 80 nC is uniformly distributed along the x axis from x = 0 to x = 2.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 8.0 m.
A) 30 N/C
B) 15 N/C
C) 48 N/C
D) 90 N/C
E) 60 N/C

Question

Quizplus · Accepted Answer

First, we need to find the expression for the electric field from a uniformly distributed charge along the x axis. Consider a small section of the charge dx located at a distance x from the point where we want to find the electric field. The magnitude of the electric field due to this small section of charge is given by:
dE = k*dx*q/x^2, where q is the charge in that small section of length dx, k is the Coulomb constant, and x is the distance between the small section of charge and the point where we want to find the electric field. 
We can substitute the given value of q, k, and x in this equation to find dE. If we integrate this expression along the length of the charge, we can find the total electric field due to the entire charge:
E = ∫(k*q/x^2)dx, from x=0 to x=2m
E = k*q ∫(1/x^2)dx, from x=0 to x=2m
E = k*q*(-1/x), from x=0 to x=2m
E = k*q*(1/0 - 1/2m)
E = 9.0*10^9 Nm^2/C^2 * 80*10^-9 C * (1/0 - 1/2)
E = 720 N/C
The magnitude of the electric field at x=8m would be the same as the electric field due to a point charge of 80 nC located at x=2m. So, we can use the expression for electric field from a point charge:
E = k*q/r^2
E = 9.0*10^9 Nm^2/C^2 * 80*10^-9 C / (8m - 2m)^2
E = 15 N/C 
Therefore, the correct choice is B.

A Charge of 80 NC Is Uniformly Distributed Along the X