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 AB . If the particle C is displaced by a distance x along the line AB , determine the magnitude of the electric force experienced by it.
Options
- AQ q d x 4 ₀ ( d^2 4 - x^2 )^2
- B2 Q q d x ₀ ( d^2 4 - x^2 )^2
- CQ q x 2 ₀ ( d^2 4 - x^2 )^2
- DQ q d x 2 ₀ ( d^2 4 - x^2 )^2
Correct answer
D. Q q d x 2 ₀ ( d^2 4 - x^2 )^2
Step-by-step solution
Let the positions of particles A and B be at - d 2 and d 2 respectively, with the origin at the midpoint. When particle C is displaced by a distance x towards B , its new distance from A is d 2 + x and from B is d 2 - x . The electric force on C due to A is F_A = 1 4 ₀ Q q ( d 2 + x )^2 directed towards B . The electric force on C due to B is F_B = 1 4 ₀ Q q ( d 2 - x )^2 directed towards A . The net electric force experienced by C is the difference between these two forces: F = F_B - F_A = Q q 4 ₀ [ 1 ( d 2 - x )^