A charge +q is placed at each of the points x = x₀, 3x₀, 5x₀, … to infinity on the x-axis, and a charge -q is placed at x = 2x₀, 4x₀, 6x₀, … to infinity. Here x₀ is a positive constant. Take the electric potential at a point due to a charge q at a distance r from it to be Q/ $4\pi\varepsilon_{\omicron}r$ Find the electric potential at the origin.
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Question

A charge +q is placed at each of the points x = x₀, 3x₀, 5x₀, … to infinity on the x-axis, and a charge -q is placed at x = 2x₀, 4x₀, 6x₀, … to infinity. Here x₀ is a positive constant. Take the electric potential at a point due to a charge q at a distance r from it to be Q/ $4\pi\varepsilon_{\omicron}r$ Find the electric potential at the origin.

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G1 Physics · Accepted Answer

Step 1: Use V = Σ[kqᵢ/rᵢ] for discrete charges or integrate dV = k dq/r for a continuous distribution. If a field is given, use ΔV = -∫𝐄·d𝐥. Step 2: Potential is a scalar, so contributions add algebraically. Step 3: Insert the stated distances/charge distribution and simplify. Final: Option D. In this specific setup, apply the calculation to: A charge + q is placed at each of the points x= x₀, x = 3x0, x = 5x0,...., and infinitum on the x-axis, a.