Two equal positive charges +q sit at y = -a and y = +a. a) Find the electric fie

Question

Two equal positive charges +q sit at y = -a and y = +a. a) Find the electric field at an arbitrary point on the r axis, and find its asymptotic form when x a(far from the pair of charges). Explain the latter result intuitively. b) Repeat for a positive charge +q at y = +a and a negative charge -q at y = -a. a) Repeat for two equal positive charges +q sitting at y = -a and y = +a, and a third charge of -2q at the origin. Note that in this arrangement, the net charge is zero (so we expect no monopolar field far away). The two visible dipoles also cancel, so we expect no dipoler field for away. What might we call the first surviving term in the distant field? (Note that there are four monopoles in this distribution.)

Explanation / Answer

a) at x distance from origin,

Ex = 2*k*q*cos(theta)/(a^2 + x^2)

= 2*k*q*x/(a^2 + x^2)^(3/2)

at x<<a, Ex = 2*k*q*x/a^3

at x>>a, Ex = 2*k*q/x^2

b) at x distance from origin,

Ex = 2*k*q*sin(theta)/(a^2 + x^2)

= 2*k*q*a/(a^2 + x^2)^(3/2)

at x<<a, Ex = 2*k*q/a^2

at x>>a, Ex = 2*k*q*a/x^3

c) unable to understand, what to find.

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