A charge +q is located at the origin, while an identicalcharge is located on the

Question

A charge +q is located at the origin, while an identicalcharge is located on the x axis at x=+0.253 m. A third charge of+2q is located on the x axis at such a place that the netelectrostatic force on the charge at the origin doubles, itsdirection remaining unchanged. What is the distance from the thirdcharge to the origin? I'm not quite sure where to start other than drawing apicture. I know that i need to use Coulomb's law but i wasn't surewhere to go from there. A charge +q is located at the origin, while an identicalcharge is located on the x axis at x=+0.253 m. A third charge of+2q is located on the x axis at such a place that the netelectrostatic force on the charge at the origin doubles, itsdirection remaining unchanged. What is the distance from the thirdcharge to the origin? I'm not quite sure where to start other than drawing apicture. I know that i need to use Coulomb's law but i wasn't surewhere to go from there.

Explanation / Answer

Let the third charge be placed at a distance d from the secondcharge The force between the charge at the origin and the charge at x= 0.253 m is F1 = k * (q * q/r2) k = (1/4o) = 9 * 109Nm2/C2 and r = (0.253 - 0) m = 0.253 m The force between the charge at the origin and the thirdcharge is F2 = k * (q * 2q/(r + d)2) The net electrostatic force on the charge at the origindoubles therefore we get (F1/F2) = 2 or F1 = 2F2 or k * (q * q/r2) = 2 * k * (q * 2q/(r +d)2) or k * (q2/r2) = (4k * q2/(r+ d)2) or (1/r2) = (4/(r + d)2) or (1/r2) = (4/(r + d)2) or (r + d)2 = 4r2 or r2 + 2rd + d2 = 4r2 or d2 + 2rd - 3r2 = 0 r = 0.253 m or d2 + 2 * 0.253 * d - 3 * (0.253)2 =0 or d2 + 0.506d - 0.192 = 0 solving the above quadratic equation we get d1 = 0.252 m and d2 = -0.758 m Therefore,the third charge should be placed 0.758 m in theopposite direction. or d2 + 2rd - 3r2 = 0 r = 0.253 m or d2 + 2 * 0.253 * d - 3 * (0.253)2 =0 or d2 + 0.506d - 0.192 = 0 solving the above quadratic equation we get d1 = 0.252 m and d2 = -0.758 m Therefore,the third charge should be placed 0.758 m in theopposite direction.

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