Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential
Determine the magnitude of the electric field at point P in the configurations illustrated in the figure for d a . Assume 2qa = p .
Options
- A(a) q 2 ₀ d^2 (b) p 2 ₀ d^3 (c) 1 2 ₀ d^3 q^2 d^2 + p^2
- B(a) q 4 ₀ d^2 (b) p 4 ₀ d^3 (c) 1 4 ₀ d^3 q^2 d^2 + p^2
- C(a) q 4 ₀ d^2 (b) 2p 4 ₀ d^3 (c) 1 4 ₀ d^3 q^2 d^2 + 4p^2
- D(a) q 4 ₀ d^2 (b) p 4 ₀ d^3 (c) 1 4 ₀ d^3 (qd + p)
Correct answer
B. (a) q 4 ₀ d^2 (b) p 4 ₀ d^3 (c) 1 4 ₀ d^3 q^2 d^2 + p^2
Step-by-step solution
For configuration (a): The electric field at point P due to a point charge q at distance d is: E_a = 1 4 ₀ q d^2 For configuration (b): The system is an electric dipole with charges -q and +q separated by 2a . Point P is on the equatorial line at distance d . The electric field for d a is: E_b = 1 4 ₀ p d^3 where p = 2qa is the dipole moment. For configuration (c): The system has three charges: -q at x = -a , +q at x = 0 , and +q at x = a . Point P is at (0, d) . The field due to the central charge +q is: E ₁ = 1 4