Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential
Two particles A and B , each carrying a charge Q , are held fixed with a separation d between them. A particle C having mass m and charge q is kept at the midpoint of the line segment AB . Particle C is displaced through a small distance x ( x d ) perpendicular to AB and then released. Assuming Q and q possess opposite signs such that the particle executes simple harmonic motion, find the time period of the oscillati
Options
- A( m ^3 ₀ d^3 Qq )^ 1/2
- B( 4m ^3 ₀ d^3 Qq )^ 1/2
- C( m ^2 ₀ d^3 Qq )^ 1/2
- D( m ₀ d^3 4Qq )^ 1/2
Correct answer
A. ( m ^3 ₀ d^3 Qq )^ 1/2
Step-by-step solution
Let the charges Q be placed at (-d/2, 0) and (d/2, 0) . The particle C is displaced to (0, x) along the perpendicular bisector. The distance of C from each charge Q is r = (d/2)^2 + x^2 . The attractive electrostatic force between C and each charge Q is F = 1 4 ₀ Qq r^2 . The components of the forces parallel to AB cancel each other, while the components perpendicular to AB add up to provide the restoring force. The net restoring force is F_ net = 2F , where = x r . F_ net = 2 ( 1 4 ₀ Qq r^2 ) ( x r ) = 2Qqx 4 ₀ r^