Point charges of magnitude `9muC` each are placed along the X-axis at x =1m , x=2m , x=4 m , x=8 m and so on till infinity . Calculate the net force experienced by a charge of 0.1 C placed at the origin.

Explanation

To solve the problem, we need to calculate the net force experienced by a charge of \(0.1 \, C\) placed at the origin due to an infinite series of point charges of \(9 \, \mu C\) located at \(x = 1 \, m, 2 \, m, 4 \, m, 8 \, m, \ldots\).

### Step-by-Step Solution:

1. **Identify the Charges and Their Positions:**
The charges are placed at positions \(x = 1 \, m, 2 \, m, 4 \, m, 8 \, m, \ldots\) which can be expressed as \(x = 2^n\) for \(n = 0, 1, 2, 3, \ldots\). Each charge has a magnitude of \(q = 9 \, \mu C = 9 \times 10^{-6} \, C\).

2. **Use Coulomb's Law to Calculate the Force:**
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