A charge is uniformly distributed with a constant line charge density lambda alo

Question

A charge is uniformly distributed with a constant line charge density lambda along the x axis from x = 1/2 L to x = L. A second charge is again uniformly distributed but with a constant line charge density -lambda along the x axis from x = - L to x = -1/2 . Please note (lambda > 0). Of course, one can try to use Gausss law to find the electric field. Is Gausss law useful for the given problem? Explain your answer. Find the electric field at point (0,0). Please use the direct integration to find out the electric field. A non-conducting sphere centered at the origin has a net charge of Q (Q > 0) on it with a volume charge density of rho and a radius of R1. The sphere is centered inside of a thick conducting spherical shell with an inner radius of R2 and an outer radius of R3. The spherical shell has a net charge of - Q on it. What is the magnitude and direction of the electric field as a function of r (distance from the origin) at the following distance ranges from the origin: r

Explanation / Answer

1)

b)

dE = -2 k dq/x^2

dq = lamda dx

E = int{-2 k lamda dx/x^2} ; from L/2 to L

E = {-2 k lamda (-1/x)} ; from L/2 to L

E = 2 k lamda ((1/L) - (2/L))

E = -2 k lamda/L

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2)

a)

E = k q/r^2

q = Q * (r/R1)^3

==> E = k (Q * (r/R1)^3)/r^2

==> E = k Q (r/R1^3)

b)

E = k Q/r^2

c)

E = 0

(Electric field inside a conductor is zero)

d)

E = k (Q-Q)/r^2

==> E = 0

e)

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