We are given the following information.
Current = 4.50 A
Length of wire = 2 m
Magnetic field = 8i T
We are asked to find the magnetic force on the wire.
Recall that the magnetic force is given by
[tex]F=i\cdot\vec{L}\times\vec{B}\sin\theta[/tex]
Where θ is the angle between the magnetic field and the wire.
Notice that the magnetic field and wire in the horizontal (x) direction are parallel meaning that the angle between them is 0° hence, there will be no magnetic force acting in the x-direction.
On the other hand, the magnetic field and wire in the vertical (y) direction are perpendicular meaning that the angle between them is 90° hence maximum magnetic force will be acting in the y-direction.
[tex]\begin{gathered} F=4.5\cdot(2j\times8i)\sin(90\degree) \\ F=4.5\cdot(2j\times8i)(1) \\ F=4.5\cdot(16k) \\ F=72k\;N \end{gathered}[/tex]
Therefore, the magnetic force acting on the wire is 72k N.
Option B is the correct answer.
