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Two short dipoles A and B are placed with their centres 80 cm apart. Dipole A has charges ±2 μC and length 1 cm. Dipole B has charges ±4 μC and length 1 cm. Find the electric field at a point P, equidistant from the centres of both dipoles.

Two short dipoles A and B are placed with their centres 80 cm apart. Dipole A has charges ±2 μC and length 1 cm. Dipole B has charges ±4 μC and length 1 cm. Find the electric field at a point P, equidistant from the centres of both dipoles.

Options:

(1) (5 × 10⁹) / 16 (2) 4.5 × 10⁴ (3) 4 × 10⁹ (4) (4 × 10⁹) / 16

Solution:

Distance from each dipole: r = 40 cm = 0.4 m Dipole moment: p₁ = 2 × 10⁻⁶ × 10⁻² = 2 × 10⁻⁸ p₂ = 4 × 10⁻⁶ × 10⁻² = 4 × 10⁻⁸ Electric field of short dipole: E = (1 / 4πε₀) × (2p / r³) Substitute: E = (9 × 10⁹ × 4 × 10⁻⁸) / (0.4)³ After simplification: E = (4 × 10⁹) / 16

Final Answer:

Correct Option: (4)
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