Question # Equal charges q are placed at the vertices ( A ) and ( B ) of an equilateral triangle ( A B C ) of side ( a ). The magnityde ( f ), magnitude of electric field at the point cis.

# Equal charges q are placed at the vertices ( A ) and ( B ) of an equilateral triangle ( A B C ) of side ( a ). The magnityde ( f ), magnitude of electric field at the point cis.

(A) ( frac{K q}{a^{2}} )

(B) ( frac{sqrt{3} K q}{a^{2}} )

( (C)sqrt{8} frac{sqrt{2} K q}{a^{2}} )

(D) ( frac{q}{2 pi t varepsilon_{0} a^{2}} )

Solution

( begin{aligned} E_{n e t} &=sqrt{E_{A}^{2}+E_{B}^{2}+2 E_{A} E_{B} cos theta} &=sqrt{2 E^{2}+2 E_{C D B}}=sqrt{2 E^{2}(1+cos theta)} &=2 E cos frac{partial}{2} &=2 frac{k Q}{a^{2}} cos left(frac{60}{2}right)=2 frac{k Q}{a^{2}} frac{sqrt{3}}{2} &=frac{sqrt{3} k Q}{a^{2}} end{aligned} )

Opfion ( b )