One plastic rod with length L and carrying a uniformly distributed charge -Q is

Question

One plastic rod with length L and carrying a uniformly distributed charge -Q is placed on the x-axis such that one end is on the origin and the other end is on the point x = -L. Another plastic rod with length L and carrying a uniformly distributed charge +Q is placed right next to the negatively charged line such that one end is on the origin and the other end is on the point x = L. The setup is shown below. Find the magnitude and direction of the electric field at a point P a distance D away from the end of the positively-charged rod as shown below. Express your answer in terms of Q, L, D and other known constants (i. e. k or epsilon_0). (Try using the result from Problem 1 and use superposition from the two individual rods). Find the magnitude and direction of the acceleration of a proton placed at point P. Express your answer in terms of the above constants, as well as the fundamental charge, ( and the mass of the proton m_p.

Explanation / Answer

electric field on the axis of a finite line of charge of length L

E = (k*Q/L)* (1/r - 1/r+L )

for the rod with +Q , the distance of P from the end = r = L

E+ = (k*Q/L)*( 1/D - 1/D+L)

for the rod with -Q , the distance of P from the end = r = D+L

E- = -(k*Q/L)*( 1/D+L - 1/D+2L)

Enet = E+ + E-

Enet = (k*Q/L)*( 1/D + 1/D+L - 1/D+L + 1/D+2L )

Enet = (k*Q/L)*( 1/D + 1/D+2L ) <<<_---------------answer

(b)

force acting on the proton = F = E*e = m*a

a = Fe/mp = Enet*e/mp

a = [ (k*Q/L)*( 1/D + 1/D+2L )*e ] / mp

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