Figure 1: Diagram showing the physical situation of a line of charge with a unif

Question

Figure 1: Diagram showing the physical situation of a line of charge with a uniform charge density.

Find the electric field in terms of L, r, Q, and

?o, at point P of a rod with length, L, and total

charge, Q, a distance r from the center of the rod along the axis of the rod when r

> L/2, as seen in

Figure 1: Diagram showing the physical situation of a line of charge with a uniform charge density. Find the electric field in terms of L, r, Q, and ?o, at point P of a rod with length, L, and total charge, Q, a distance r from the center of the rod along the axis of the rod when r > L/2, as seen in Figure 1.

Explanation / Answer

take a small cut of the rod dx

this will have dq = dx Q/L

it will also give a dE

dE = 1/( 4pi e0) dq/x^2

E = 1/(4 pi e0) integral of Q/L dx/x^2 from r to r + L

E = Q/( 4 pi L e0) - 1/x from r to r+L

E=Q/( 4 pi L e0) *( 1/r - 1/(r +L))

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