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An equilateral triangle wire frame of side L having 3 point charges at its vertices is kept inx-y plane as showm Component of electric field due to the configuration in z direction at (0, 0, L ) is [origin is centroid of triangle ]

Answer»

` ( 9sqrt 3 KQ)/(8L^2)`
zeri
` (9kq)/(8L^2)`
None

Solution :` vec E+p (Kq)/(|vec r_2 -vec r_1|^3). (vec r_2 - vec r_1)`
` r_(PA) = r_(rB) =R _(PC = sqrt ((L/(sqrt3) )^2 +L^2) = (2L)/(sqrt 3)`
` vec E_P = ve cE_(PA) + vec E_(PE) + vec E_(Pc)`

`vecE_(PA) =(Kq)/(r_(PA)^(3))vecrPA =(Kq)/(r^(3) ) (-(1)/(sqrt3) hat j +Lhat k)`
` vec E_(PB) = (Kq)/r^3 (1/2 hat i + 1/(2sqrt 3) hat j + L hat k)`
` vec E_(PC) = (2Kq)/r^3 (- 1/2 hat i + 1/(2sqrt3) hat j + L hat k)`
`E_(P(z))=E_(PA(z) +E_(PB(z))+E+(PC_(z)=0`


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