Question

Three point charges of `+2muC, -3muC` , and `-3muC` are kept at the vertices A, B, and C, respectively of an equilateral triangle of side 20 cm. what should be the sign and magnitude of the charge (q) to be placed at the midpoint (M) of side BC so that the charge at A remains in equilibrium?

Answer 1

Let a charge q be placed at 0, as shown in Fig.

Now, `vec(F)_(AB) = (q_(1) q_(2))/(4pi in_(0) AB^(2))`
`= (9xx10^(9)xx(2xx10^(-6))(3xx10^(-6)))/((0.20)^(2))`
`vec(F)_(AB) = 1.35N`, along AB
`vec(F)_(AC) = (q_(1) q_(2))/(4pi in_(0) AC^(2)) = (9xx10^(9)xx(2xx10^(-6))(3xx10^(-6)))/((0.20)^(2))`
= 1.35N, along AB
`vec(F)_(AO) = (q_(1) (q))/(4pi in_(0) AO^(2)) = (9xx10^(9) (2xx10^(-6)) q)/((sqrt(3) xx 10^(-1))^(2))`
`= 6xx10^(5)` q, along OA, when q is positive For equilibrium of charge at A,
`F_(AB) cos 30^(@) + F_(AC) cos 30^(@) = F_(AO)`
`1.35 (sqrt(3))/(2) + 1.35 xx(sqrt(3))/(2) = 6xx10^(5)q`
`:. q = (1.35 sqrt(3))/(6xx10^(5)) = 0.3897xx10^(-5) C = 3.897 muC`