Four equal positive charges

PHYSICS · Single correct · AP · Physics C: Electricity and Magnetism · Electric Charges Fields and Gauss's Law · Electric Charges Fields and Gauss's Law

Problem

Four equal positive charges, each of value QQ, are arranged at the four corners of a square of diagonal 2a2a. A small body of mass mm carrying a unit positive charge is placed at a height hh above the center of the square. What should be the value of QQ in order that this body may be in equilibrium? (1) πϵ0mg2h(h2+2a2)3/2\pi\epsilon_0 \frac{mg}{2h} (h^2 + 2a^2)^{3/2} (2) πϵ0mgh(h2+a2)3/2\pi\epsilon_0 \frac{mg}{h} (h^2 + a^2)^{3/2} (3) πϵ02mgh(h2+2a2)3/2\pi\epsilon_0 \frac{2mg}{h} (h^2 + 2a^2)^{3/2} (4) πϵ0mg2h(h2−a2)3/2\pi\epsilon_0 \frac{mg}{2h} (h^2 - a^2)^{3/2}

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