Beginning physics, in finding the electric field for a uniform line charg

[krtica]

Q:
A uniform line charge that has a linear charge density λ = 4.4 nC/m is on the x-axis between x = 0 to x = 5.0 m.
(a) What is its total charge?

(b) Find the electric field on the x-axis at x = 6 m.

(c) Find the electric field on the x-axis at x = 11.0 m.

(d) Find the electric field on the x-axis at x = 240 m.


To solve for a, I used the equation Q=lambda*length. My answer is 22nC, which is correct.

To solve for the remaining portion of the question, I used E=kQ/[x^2], where I took x to be (L+a-x). L is defined as the length of the rod (5m), a is the difference between the given position and the rod (for b, 1m), and x is the distance from the origin to the midpoint of the rod (2.5m).

 

[ideasrule]

To solve for the remaining portion of the question, I used E=kQ/[x^2], where I took x to be (L+a-x). L is defined as the length of the rod (5m), a is the difference between the given position and the rod (for b, 1m), and x is the distance from the origin to the midpoint of the rod (2.5m).

The fact that you didn't get the right answer proves that E=kQ/[x^2] can only be used for point masses, not for extended objects. (The sphere is an exception, but that's a special case.) To solve this problem, you have to use calculus. What's the charge contributed by a length "dx" of rod a distance "x" from the given position?