Question

A wire carries a 11.3-mA current along the +x-axis through a magnetic field = (16.2 + 2.4 ĵ) T. If the wire experiences a force of -15.7 N as a result, how long is the wire?

Answer 1

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

$B = \sqrt{16.2^2 +2.4^2} = \sqrt{268.2} = 16.377 \ T$

$tan \theta = \frac{2.4}{16.2} \\\\tan \theta = 0.1482\\\\\theta = tan^{-1}(0.1482) \\\\\theta = 8.43^o$

Length of the wire is calculated as;

$L = \frac{F}{BIsin \theta} = \frac{15.7}{16.377*11.3*10^{-3}*sin(8.43)} = 578.9 \ m$

Therefore, the length of the wire is 579 m