A point charge q₁ = 4q₀ is placed at origin. Another point charge q₂ = −q₀ is placed at x = 12 cm. Charge of proton is q₀. The proton is placed on x-axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is _____ cm. Image
Physics · Circular Motion
JEE Mains 29 January 2023 Shift 1 Morning Shift

Question

A point charge q₁ = 4q₀ is placed at origin. Another point charge q₂ = −q₀ is placed at x = 12 cm. Charge of proton is q₀. The proton is placed on x-axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is _____ cm. Image

Physics · Circular Motion

JEE Mains 29 January 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

The zero-field point lies to the right of q₂. Let its distance from q₂ be x. Then its distance from q₁ is x+12. Equating field magnitudes: 4/(x+12)² = 1/x². Hence x+12 = 2x, giving x = 12 cm. Therefore position from origin = 12+12 = 24 cm.