please include a drawing of the charge distribution and the point at which the E

Question

please include a drawing of the charge distribution and the point at which the E-field is being evaluated.

please include a sample vector diagram, showing the electric-field vectors for critical dq's.

how to explain any cancellations due to symmetry?

Thank you for your help.

Problem A: As shown in the figure, an insulating rod of length L has charge -q uniformly distributed along its length. a. b. c. What is the linear charge density of the rod? What is the electric field at point P, a distance a from the end of the rod? If P were very far from the rod, the rod would look like a point charge. Show that your answer to part b reduces to the electric field of a point charge for a >L

Explanation / Answer

(A) linear charge density, lambda = - q / L

(B) lets take a element of length dx.

dq = lambda dx = -q dx / L

dE = k dq / (a + x)^2

E = integral of (kq/L) ) (dx / (a + x)^2)

E = - (k q / L) [1 / a - 1/(a + L)]

E = - k q / (a (a + L)) ......Ans

(C) E = - k q / ( a^2 (1 + L/a))

L/a > > 1

1 + L/a = 1

E = - k q / a^2

  

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