Question

In a long straight wire, what current is required to exert a 1.0μN force on a 1.0μC charge moving at 1.5×106m/s parallel to the wire at a distance of 0.35m from the wire?

Answer 1

Answer:

Current in the wire is given as

$i = 1.17 \times 10^{-7} A$

Explanation:

magnetic field due to long current carrying wire is given as

$B = \frac{\mu_0 i}{2\pi r}$

so we have magnetic force on moving charge is given as

$F = qvB$

so we have

$F = (1\times 10^{-6})(1.5 \times 10^6)(\frac{\mu_0 i}{2\pi (0.35)})$

so we have

$1\times 10^{-6} = 1.5 \times \frac{2 i}{0.35}$

$i = 1.17 \times 10^{-7} A$