Along x-axis at positions `x=1,x=2,x=4…………oo` charges q is placed. What will be electric field at x=0 due to these charges. What will be the value of electric field If the charges are alternately positive and negative.

Explanation

To find the electric field at \( x = 0 \) due to an infinite number of charges placed at positions \( x = 1, 2, 4, 8, \ldots \) along the x-axis, we can follow these steps:

### Step 1: Understand the Configuration
We have an infinite series of charges \( q \) placed at positions \( x = 1, 2, 4, 8, \ldots \). The distances from the origin (where we want to find the electric field) are \( r_1 = 1, r_2 = 2, r_3 = 4, r_4 = 8, \ldots \).

### Step 2: Calculate the Electric Field Contribution from Each Charge
The electric field \( E \) due to a point charge \( q \) at a distance \( r \) is given by:
\[
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