Final answer:
The x-component of the force exerted on the second particle by the first particle depends on the product of their charges and the distance between them. The value of d at which the x-component of the force is the greatest can be found by taking the derivative of the force equation and setting it equal to zero.
Step-by-step explanation:
The x-component of the force exerted on the second particle by the first particle can be found using Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
In this case, the charge of the first particle is Q, and the charge of the second particle is q. The distance between them on the x-axis is d. So, the force on the second particle can be expressed as F = k * (Q * q) / d^2, where k is Coulomb's constant.
To find the value of d at which the x-component of the force is the greatest, we can take the derivative of this equation with respect to d and set it equal to zero. Solving this equation will give us the value of d that maximizes the x-component of the force.