A long straight wire is carrying a current of 20 A. An electron is moving with a speed of \( 10^{7}\,\mathrm{m/s} \) parallel to the wire. The force experienced by the electron when it is 2 cm away from the wire is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 3.2 \times 10^{-16}\,\mathrm{N} \)
The field of a long straight wire is \( B = \mu_0 I/2\pi r \), in circles around the wire. An electron moving parallel to the wire moves perpendicular to this field, so the magnetic force is \( F = evB \).
\( \displaystyle r = 2\,\mathrm{cm} = 0.02\,\mathrm{m} \)
\( \displaystyle B = \frac{\mu_0 I}{2\pi r} = \frac{4\pi\times10^{-7} \times 20}{2\pi \times 0.02} = 2\times10^{-4}\,\mathrm{T} \)
\( \displaystyle F = evB = 1.6\times10^{-19} \times 10^{7} \times 2\times10^{-4} = 3.2\times10^{-16}\,\mathrm{N} \)