A stiff wire 35.5 cm long is bent at a right angle in the middle. One section lies along the z-axis and the other is along the line y=2x in the xy-plane. A current of 22.5 A flows in the wire-down the z-axis and out the line in the xy-plane. The wire passes through a uniform magnetic field given by B = (.318 i)T.
Determine the magnitude and the direction of the total force on the wire.

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Vespertilio Vespertilio · Answer 1 · 2020-03-24T07:57:32+01:00

Answer:

Explanation:

Length, l = 35.5 cm = 0.355 m

y = 2 x

Slope, y / x = 2

tan θ = 2

θ = 63.4°

i = 22.5 A

B = 0.318 i Tesla

[tex]\overrightarrow{l}=0.355\widehat{k}+0.355 Cos63.4\widehat{i}+0.355 Sin63.4\widehat{j}[/tex]

[tex]\overrightarrow{l}=0.16\widehat{i} + 0.32\widehat{j}+0.355\widehat{k}[/tex]

[tex]\overrightarrow{B}=0.318\widehat{i}[/tex]

The magnetic force is given by

[tex]\overrightarrow{F}=i(\overrightarrow{l}\times \overrightarrow{B})[/tex]

[tex]\overrightarrow{F}=22.5\left ( 0.16\widehat{i}+0.32\widehat{j}+0.355\widehat{k} \right )\times 0.318\widehat{i}[/tex]

[tex]\overrightarrow{F}=2.54\widehat{j}-2.29\widehat{k}[/tex]

Magnitude of force

[tex]F=\sqrt{2.54^{2}+2.29^{2}}[/tex]

F = 3.42 N

The angle is Ф

tanФ = -2.29/2.54

Ф = 42° below y axis