Here are the exact directions of this problem: \"A rod that is 30 cm. long is gi

Question

Here are the exact directions of this problem:

"A rod that is 30 cm. long is given a uniformly distributed charge Q= 5 x 10-6C. Compute

the potential at a point P, which is a distance 15 cm. from the end of the road assuming

that V = 0 at infinity. See figure 1."

Here is the diagram:   

P ---------------- _______________________

         15 cm.                  Rod, L= 30 cm.

" A quick explanation of the diagram: P obviously represents point p, the dashed line represents the 15cm. distance between the end of the rod and the point, and the solid line obviously represents the rod."

Please give me a detailed, thorough answer with step by step instructions. Thanks! Note: this is not a homework problem or a problem directly from the book.

Explanation / Answer

Since V = kq/r, we know dV = k dq/r, and if we let be the linear charge density then dV = k dr/r.

Call r1 the distance from p to the near end of the rod and r2 the distance to the far end, then

V = k dr/r where the integral is taken from r1 to r2

= k (ln r2 - ln r1) = k ln(r2/r1) =

(8.99 * 109 Nm2/C2)(5.0 * 10-6 C/0.30 m) ln (45/15) = 1.65 * 105 V

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