Question

Consider the charges q,q and -q placed at the vertices of an equilateral triangle of each side l. What is the force on each charge ?
A. `q^(2)/(4sqrt2piepsilon_(0)l^(2))`
B. `(-q^(2))/(4piepsilon_(0)l^(2))`
C. `(q^(2))/(4piepsilon_(0)l^(2))`
D. zero

Answer 1

Correct Answer - D
From diagram, force on `q_(1)(=q)` at A,

`vecF_(1)=vecF_(12)+vecF_(13)=Foverset(""^^)(r)_(1)`
where `F=q^(2)/(4piepsilon_(0)l^(2))and oversetwedge(r)_(1)`, is the unit vector along BC
Force on `q_(2)(=q)` at B, `vecF_(2)=vecF_(21)+vecF_(23)=Foversetwedge(r)_(2)`
(where `oversetwedge(r)_(2)` is the unit vector along AC)
Force on `q_(2)(=-q)` at C,
`vecF_(3)=vecF_(31)+vecF_(32)=(sqrt(F^(2)+F^(2)+2F Fcos60^(@)))oversetwedge(n)=sqrt3Foversetwedge(n)`
where `oversetwedge(n)` = unit vector along the direction bisecting `angleBCA`
`therefore" "vecF_(1)+vecF_(2)+vecF_(3)=0`