A charge q = 1 mC is placed at point (1 m, 2 m, 4 m). Find the elec...

Question

A charge q = 1 mC is placed at point (1 m, 2 m, 4 m). Find the electric field at point P(0 m, -4 m, 3 m).

Accepted Answer

Given:
• q = 1 mC = 10⁻³ C
• Source position A(1, 2, 4)
• Field point P(0, -4, 3)

Step 1: Find position vector from charge to P
r = P - A = (0-1, -4-2, 3-4)
r = (-1, -6, -1)

Step 2: Find magnitude of r
|r| = √[(-1)² + (-6)² + (-1)²]
|r| = √(1 + 36 + 1)
|r| = √38 m

Step 3: Apply electric field formula
E = kq · r / |r|³

Step 4: Substitute values
E = (9 × 10⁹) × (10⁻³) × (-1, -6, -1) / (√38)³
E = (9 × 10⁶) × (-1, -6, -1) / (38√38)
E = (9 × 10⁶) / (38 × 6.16) × (-1, -6, -1)
E ≈ 3.84 × 10⁴ × (-1, -6, -1) N/C

Final Answer:
E ≈ -3.84 × 10⁴ î - 23.04 × 10⁴ ĵ - 3.84 × 10⁴ k̂ N/C

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