Two charges, q 1 and q 2, are located at the origin and at (0.65 m , 0), respect

Question

Two charges, q1 and q2, are located at the origin and at (0.65 m , 0), respectively.

a)Where on the x-axis must a third charge, q3, of arbitrary sign be placed to be in electrostatic equilibrium if q1 and q2 are like charges of equal magnitude? ____m

b) Where on the x-axis must a third charge, q3, of arbitrary sign be placed to be in electrostatic equilibrium if q1 and q2 are unlike charges of equal magnitude?_____m

c) Where on the x-axis must a third charge, q3, of arbitrary sign be placed to be in electrostatic equilibrium if q1 = +2.5 C and q2 = -6.0 C ?___m

Explanation / Answer

a) The charge q3 must be placed at distance X from the origin such that
kq1/X^2 = kq2/ (0.65 - X )^2
since q1 = q2
( 0.65 - X ) ^2 = X^2
0.65^2 - 1.3 X + X^2 = X^2
0.65/1.3 = X = 0.5 m

b) if q1 and q2 are unlike charges of equal magnitude

then (k*|q1|)/d² = (k*|q2)/{(d+0.65})² or
(d + 0.65)/d = (q2/q1) = +-(1)
-d = d+ 0.65 or
d = -0.325 m

c)  Electric field due to q1 and q2 will be zero x< 0, a distance of d away from q1 so that x = -d; have
(k*|q1|)/d² = (k*|q2)/{(d+0.65})² or
(d + 0.65)/d = (q2/q1) = (6.0/2.5) = 1.55 or
d*1.55 = d+ 0.65 or
d = 1.18 m
So a charge q3 of any magnitude or sign can be be kept at x = -1.18 m to be in equilibrium.

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