An infinite number of charges each q are placed in the x-axis at distances of 1, 2, 4, 8, ………meter from the origin. If the charges are alternately positive and negative find the intensity of electric field at origin.

Explanation

To find the intensity of the electric field at the origin due to an infinite number of charges placed alternately on the x-axis at distances of 1, 2, 4, 8, ..., we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charge Configuration**:
- The charges are placed at distances of \(1, 2, 4, 8, \ldots\) meters from the origin. This forms a geometric series where the distances are \(d_n = 2^{n-1}\) for \(n = 1, 2, 3, \ldots\).
- The charges are alternately positive and negative: \(+q, -q, +q, -q, \ldots\).

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