Answer:
Approximately [tex]7.3 \times 10^{-3}\; \rm A[/tex] (approximately [tex]7.3\; \rm mA[/tex]) assuming that the magnetic field and the wire are both horizontal.
Explanation:
Let [tex]\theta[/tex] denote the angle between the wire and the magnetic field.
Let [tex]B[/tex] denote the magnitude of the magnetic field.
Let [tex]l[/tex] denote the length of the wire.
Let [tex]I[/tex] denote the current in this wire.
The magnetic force on the wire would be:
[tex]F = B \cdot l \cdot I \cdot \sin(\theta)[/tex].
Because of the [tex]\sin(\theta)[/tex] term, the magnetic force on the wire is maximized when the wire is perpendicular to the magnetic field (such that the angle between them is [tex]90^\circ[/tex].)
In this question:
Rearrange the equation [tex]F = l \cdot I \cdot \sin(\theta)[/tex] to find an expression for [tex]I[/tex], the current in this wire.
[tex]\begin{aligned} I &= \frac{F}{l \cdot \sin(\theta)} \\ &= \frac{3\times 10^{-3}\; \rm T}{6 \times 10^{-2}\; \rm m \times \sin \left(20^{\circ}\right)} \\ &\approx 7.3 \times 10^{-3}\; \rm A = 7.3 \; \rm mA\end{aligned}[/tex].
