two charged particles, A and B, are fixed in place. A third charge, C, is fized

Question

two charged particles, A and B, are fixed in place. A third charge, C, is fized in place to the right of charge B at twice the distance between A and B. There is no net force on charge C due to charges A and B. Indicate wheter each of the following statements is true, false, or cannot be determined:

Charge A has a greater magnitude than charge C:

Charge A has a greater magnitude than charge B:

Charge C has a greater magnitude than charge B:

Charge A has the same magnitude as charge C:

Charge A has the same magnitude as charge B:

Charge C has the same magnitude as charge B:

Explanation / Answer

Suppose charge A is q1 charge B is q2 charge c is q3 .

Now According to Coulomb's law F=(k*q1*q2)/r^2

As charge B is at rest despite both the forces acting from charges q1 and q3

Hence F1=F3 i.e k*q1*q2/r^2=k*q3*q2/(2*r)^2

Cancelling k,r^2 and q2 on both sides we get q3=4*q1

Hence we can't make any deduction w.r.t charge B

In 2,3,5,6 statements true or false can't be said about them

Charge C has greater magnitude than Charge A

Hence 1st and 4th statements are false

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