Question

A long straight wire carries a current of 10 A. An electron travels with velocity \(5 \times 10^6\,m\,s^{-1}\) at a distance 0.1 m from it, in a direction opposite to the current. Estimate the force experienced by the electron.

• A. \(1.6 \times 10^{-18}\,N\)
• B. \(1.6 \times 10^{-17}\,N\)
• C. \(1.6 \times 10^{-16}\,N\)
• D. \(1.6 \times 10^{-15}\,N\)

Hint:

For magnetic force problems, always check orientation to decide whether \(\sin\theta = 1\) or not.

Answer 1

The Correct Option is B

Step 1: Field from straight wire.
B = μ₀ I/(2π r) = (4π×10⁻⁷ × 10)/(2π × 0.1) = 2×10⁻⁵ T.

Step 2: Lorentz force magnitude.
F = q v B sinθ; electron moves perpendicular to B, so sinθ=1.

Step 3: Substituting values.
F = (1.6×10⁻¹⁹)(5×10⁶)(2×10⁻⁵).

Step 4: Calculation.
F = 1.6 × 10⁻¹⁷ N.

Step 5: Conclusion.
The force on the electron is 1.6 × 10⁻¹⁷ N.