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A charge 4q is at the origin, and a charge of -3q is on the positive x-axis at x = a. Where would you place a third charge so it would experience zero net electric force? (Note: Either enter your answer as an unevaluated expression, e.g., (3/2 + sqrt(3))a, or if evaluated, use 2 decimal places.) Your expression should be in terms of the given variable.

Respuesta :

Answer:

6.45 a

Explanation:

Charge on O, q1 = 4q

Charge on A, q2 = - 3 q

OA = a

Let the net force is zero at point P, where AP = x , let a charge Q is placed at P.

The force on point P due to the charge q1 = The force on point P due to the  

                                                                          charge q2

By using Coulomb's law

[tex]\frac{Kq_{1}Q}{OP^{2}}=\frac{Kq_{2}Q}{AP^{2}}[/tex]

[tex]\frac {K4qQ}{(a+x)^{2}}= \frac {K3qQ}{x^{2}}[/tex]

[tex]\frac{a+x}{x}=\sqrt{\frac{4}{3}}[/tex]

[tex]\frac{a+x}{x}=1.155[/tex]

a + x = 1.155 x

0.155 x = a

x = 6.45 a

Thus, the force is zero at x = 6.45 a.

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