Manipal MET2017PhysicsOscillations
Two equal charges q are kept fixed at a and +a alpng the x -axis. A particle of mass m and charge q 2 is brought to the origin and given a small displacement along the x -axis, then
Options
- Athe particle executes oscillatory motion
- Bthe particle remains stationary
- Cthe particle executes, SHM along x -axis
- Dthe particle executes SHM along y -axis
Correct answer
C. the particle executes, SHM along x -axis
Step-by-step solution
From Coulomb's law aligned F & = 1 4 ₀ q₁ q₂ r^2 F & = 1 4 ₀ q q 2 (a+x)^2 - 1 4 ₀ q q 2 (a-x)^2 & = 1 4 ₀ q^2 2 [ 1 (a+x)^2 - 1 (a-x)^2 ] & = 1 4 ₀ q^2 2 [- 4 a x (a^2-x^2 )^2 ] aligned When x a , then aligned & F=- 2 q^2 4 ₀ a^3 x & F -x aligned Hence, SHM along x -axis.