A charge 10⁻⁹ C is located at the origin of a Cartesian co-ordinate system and another charge Q at (2,0,0) m. If the Y-component of the electric field at (3,1,1) m is zero, the value of charge Q is C.

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(2) -0.1424×10⁻⁹. Given: q₁=10⁻⁹ C at (0,0,0); Q at (2,0,0); field point P(3,1,1). Idea: the field of a point charge is ⃗E=(kq ⃗r)/(r³), with ⃗r drawn from the charge to P, so its y-component is (kq y)/(r³). From q₁: ⃗r₁=(3,1,1), r₁=√11, so E_1y=(k(10⁻⁹)(1))/(11^3/2) From Q: ⃗r₂=(1,1,1), r₂=√3, so E_2y=(kQ(1))/(3^3/2) Set E_1y+E_2y=0: (10⁻⁹)/(11^3/2)+Q/(3^3/2)=0 Q=-10⁻⁹(3/(11))^3/2=-10⁻⁹×0.1424 Q=-0.1424×10⁻⁹ C

A charge 10⁻⁹ C is located at the origin of a Cartesian co-ordinate system and another charge Q at (2,0,0) m. If the Y-component of the electric field at (3,1,1) m is zero, the value of charge Q is _____ C.

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