Question

Two particles each with charge -Q are a fixed distance L apart, as show above. Each particle experiences a net electric force F. A particle with a charge +q is now fixed midway between the two particles. As a result the net electric force experienced by each negatively charged particle is reduced to F/2. What is the value of +q?QQ/2Q/4Q/8Q/16

Answer 1

The electric force between two charges can be calculated with the formula below (Coulomb's law):

`F_e=(K_e\cdot|q_1|\cdot|q_2|)/(d^2)`

Where Ke is the Coulomb's constant, q1 and q2 are the charges and d is the distance between them.

So, for Fe = F, q1 = q2 = Q and d = L, we have:

`F=(K_e\cdot Q^2)/(L^2)`

Now, after the addition of a positive charge in the middle of the charges, each negative charge will suffer another force, acting on the opposite direction of force F:

Since the new resulting force on the negative charges is F/2, the new force created by the positive charge addition is also F/2, so we have:

`\begin{gathered} (F)/(2)=(K_e\cdot Q\cdot q)/((L/2)^2) \\ F=(2\cdot K_e\cdot Q\cdot q)/(L^2/4) \\ F=(8\cdot K_e\cdot Q\cdot q)/(L^2) \\ (K_e\cdot Q^2)/(L^2)=(8\cdot K_e\cdot Q\cdot q)/(L^2) \\ Q=8q \\ q=(Q)/(8) \end{gathered}`

Therefore the correct option is the fourth one: q = Q/8.