Two points charges + 9e and +e are kept 16 cm apart to each other. Where a third charge q is placed between them so that the system is in the equilibrium state-

Question

in simple steps

Answer 1

To find the position of the third charge q where the system is in equilibrium, we can consider the forces acting on it.

1. The force between the charge +9e and charge q:

The force between two point charges is given by Coulomb's law: F = k * (q1 * q2) / r^2

Here, k is the electrostatic constant, q1 is the charge of the first point charge (+9e), q2 is the charge of the third point charge (q), and r is the distance between them.

Let's denote the force between +9e and q as F1.

2. The force between the charge +e and charge q:

Similar to the first case, let's denote the force between +e and q as F2.

When the system is in equilibrium, the net force on q will be zero. So, F1 + F2 = 0.

3. The equilibrium condition:

Since the force between two point charges is attractive or repulsive depending on the sign of the charges, we need to consider two possible scenarios for equilibrium:

a) If q is positive:
In this case, F1 will be attractive and F2 will be repulsive. To make their sum zero, F1 (attractive) should be equal in magnitude to F2 (repulsive).

So, F1 = F2
Using Coulomb's law, we have:
k * ((9e) * q) / (16^2) = k * ((e) * q) / ((16 - x)^2)
where x is the distance between q and the charge +e.

Simplifying this equation, we get:
9 * q / 256 = q / (256 - 32x + x^2)
9 * (256 - 32x + x^2) = 256
9x^2 - 288x + 2304 = 0

We can solve this quadratic equation to find the possible values of x. The solution will give the position of q between the two charges.

b) If q is negative:
In this case, F1 will be repulsive and F2 will be attractive. Similar to the previous case, we can set up the equation and solve it for the position of q.

By solving the respective equations, we can find the position of the charge q for the system to be in equilibrium.