Two oppositely charged point particles sit on the x axis: the particle with char

Question

Two oppositely charged point particles sit on the x axis: the particle with charge +q sits at -d/2 while the particle with charge -q sits at d/2. (a) Find the electric field on the z axis. (Your solution should include a detailed diagram of the physical situation with all relevant variables indicated.) (b) Find the limiting expression for E when z > > d. How does the dependence on distance compare to that of a single point charge (sitting at the origin)? Which falls off faster as the distance z is increased? (c) Find the limiting expression for E when z

Explanation / Answer

A) Electric field E = field due to both charges

Vertical components will be cancelled out,

E= 2kq/r^2 *(d/2r)

= 2kq/(z^2 +d^2 /4) * d/(2 sqrt (z^2 + d^2 /4))

B) if z>>>d,

E = 2 kq/z^2 *d/2z

= kq d/z^3

Here we can see it is proportional to 1/z^3 while field due to single point charge is proportional to 1/z^2

Electric field in this case falls faster than a single point charge at origin.

C) if z<<<<d,

E = 2kq/(d^2 /4)*1

= 8kq/d^2

It is expected as it is like two charges at each side

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