At the base of a smooth inclined plane with an inclination of 30^ , a particle A having a mass of 100 g and a charge of 2.0 10⁻⁶ C is placed. At what distance from the bottom along the incline should another particle B , with the same mass and charge, be positioned so that it remains in equilibrium?

Step-by-step solution

For particle B to be in equilibrium, the net force acting on it along the inclined plane must be zero. The downward component of the weight of particle B along the incline is balanced by the upward electrostatic force of repulsion from particle A. mg = 1 4 ₀ q^2 r^2 Substituting the given values m = 0.1 kg , g = 9.8 m/s ^2 , = 30^ , and q = 2.0 10⁻⁶ C : 0.1 9.8 30^ = 9 10^9 (2.0 10⁻⁶)^2 r^2 0.1 9.8 0.5 = 9 10^9 4.0 10⁻¹² r^2 0.49 = 0.036 r^2 r^2 = 0.036 0.49 0.0735 m ^2 r 0.271 m = 27.1 cm The closest value among t