Answer :
Answer:
The length of the wire is 579 m
Explanation:
Given;
current on the wire, I = 11.3-mA
magnetic field of the wire, B = (16.2i + 2.4 ĵ) T
Magnitude of force experience by the wire, F = 15.7 N
Magnitude of force experience by current carrying wire at a given a magnetic field strength is calculated as;
F = BILsinθ
Where;
B is magnitude of magnetic field
F is the force on the wire
L is length of the wire
θ is direction of the magnetic field
[tex]B = \sqrt{16.2^2 +2.4^2} = \sqrt{268.2} = 16.377 \ T[/tex]
[tex]tan \theta = \frac{2.4}{16.2} \\\\tan \theta = 0.1482\\\\\theta = tan^{-1}(0.1482) \\\\\theta = 8.43^o[/tex]
Length of the wire is calculated as;
[tex]L = \frac{F}{BIsin \theta} = \frac{15.7}{16.377*11.3*10^{-3}*sin(8.43)} = 578.9 \ m[/tex]
Therefore, the length of the wire is 579 m