Explanation:
It is given that, the magnetic field in a region of space is specified by its x, y, and z components are given by :
[tex]B_x=0.146\ T[/tex]
[tex]B_y=0.177\ T[/tex]
[tex]B_z=0.2\ T[/tex]
Length of the wire, L = 30 cm = 0.3 m (along z axis)
Current flowing through the wire, I = 3.35 A (along -z axis)
Magnetic force is given by :
[tex]F=I(L\times B)[/tex]
[tex]F=3.35(0.3k\times (0.146i+0.177j+0.2k))[/tex]
Since,
[tex]i\times j=k\\j\times k=i\\k\times i=j[/tex]
[tex]F=0.1467j-0.1778i[/tex]
[tex]|F|=\sqrt{0.1467^2+(0.1778)^2}[/tex]
|F| = 0.446 N
Direction of force:
[tex]\theta=tan^{-1}\dfrac{F_y}{F_x}[/tex]
[tex]\theta=tan^{-1}\dfrac{0.1467}{-0.1778}[/tex]
[tex]\theta=-39.52^{\circ}[/tex]
Hence, this is the required solution.
