An insulating rod extends from x = 0 to x = L, and has a non-uniform charge density lamda=A(x+d)^4?

Question

(b) Find the total charge on the rod. Answer in terms of k, A, L, and constants.

(c) Write the integral needed to find the voltage at a point x = -d. Answer in terms of k, A, L, d, and constants.

Answer 1

total charge Q

Q = integral from 0 to L of A(x+d)^4 dx

Q = A/5 ((L+d)^5 - d^5)

Voltage at x=-d

(assumes that this pt is on the rod, otherwise k is not constant)

E = 1/(4 pi k e0) * q/ r^2

r = x+d

E = integral from 0 to L of 1/(4 pi k e0) * A (x+d)^4 / (x+d)^2 dx

E = A / (4 pi k e0) * ((L+d)^3 - d^3)/3