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A long straight wire carries a certain current and produces a magnetic field of 2 × 10⁻⁴ weber/m² at a perpendicular distance of 5 cm from the wire. An electron situated at 5 cm from the wire moves with a velocity 10⁷ m/s towards the wire along perpendicular to it. The force experienced by the electron will be
- 1.6 × 10⁻¹⁷ N
- 3.2 × 10⁻¹⁷ N
- 4.8 × 10⁻¹⁷ N
- 6.4 × 10⁻¹⁷ N
Correct answer: 3.2 × 10⁻¹⁷ N
Solution
The magnetic force on a moving charge is given by F = qvB sinθ. Here, q = 1.6 × 10⁻¹⁹ C (charge of electron), v = 10⁷ m/s, B = 2 × 10⁻⁴ T, and θ = 90° (since velocity is perpendicular to the magnetic field). Substituting, F = (1.6 × 10⁻¹⁹)(10⁷)(2 × 10⁻⁴)(sin 90°) = 3.2 × 10⁻¹⁷ N.
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