Question

A straight conductor carries a current of 5 A. An electron travelling with a speed of $5\times 10^{6}\mathrm{ms}^{-1}$ parallel to the wire at a distance of $0.1\mathrm{m}$ from the conductor, experiences a force of}

• A. $8\times 10^{-20}\mathrm{N}$
• B. $3.2\times 10^{-19}\mathrm{N}$
• C. $8\times 10^{-18}\mathrm{N}$
• D. $1.6\times 10^{-19}\mathrm{N}$

Hint:

Force on a moving charge due to a current-carrying wire: $F = \frac{\mu_0 I e v}{2\pi r}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Magnetic field due to a long straight wire is $B = \frac{\mu_0 I}{2\pi r}$. Force on a moving charge is $F = evB$.
Step 2: Detailed Explanation:
$B = \frac{4\pi \times 10^{-7} \times 5}{2\pi \times 0.1} = 10^{-5}$ T.
$F = (1.6 \times 10^{-19}) \times (5 \times 10^6) \times 10^{-5} = 8 \times 10^{-18}$ N.
Step 3: Final Answer:
The force is $8 \times 10^{-18}$ N.