The expression of the magnetic force and solving the determinant allows to shorten the result for the value of the magnetic force are:
Given parameters.
To find.
The magnetic force on a wire carrying a current is the vector product of the direction of the current and the magnetic field.
F = i L x B
Where the bold letters indicate vectors, F is the force, i the current, L a vector pointing in the direction of the current and B the magnetic field.
The best way to find the force is to solve the determinant, in general, a vector (L) is written in the form of the module times a unit vector.
[tex]F= i |L| \left[\begin{array}{ccc}i&j&k\\L_x&L_y&L_z\\B_x&B_y&B_z\end{array}\right][/tex]
Let's calculate.
[tex]F= 9.00 \ 0.25 \ \left[\begin{array}{ccc}i&j&k\\0&0&1\\-0.242&-0.985&-0.336\end{array}\right][/tex]
[tex]F = 2.26 \ ( - 1 B_y i \ + 1 B_x j \ )[/tex]
F = 2.5 (0.985 i ^ - 0.242 j ^)
F = ( 2.46 i ^ - 0.605 j^ ) N
To find the magnitude we use the Pythagorean theorem.
F = [tex]\sqrt{F_x^2 + F_y^2}[/tex]
F = [tex]\sqrt{2.46^2 + 0.605^2}[/tex]
F = 2.53 N
Let's use trigonometry for the direction.
Tan θ ’= [tex]\frac{F_y}{F_x}[/tex]
θ'= tan⁻¹ [tex]\frac{F_y}{F_x}[/tex]
θ'= tan⁻¹1 ([tex]\frac{-.605}{2.46}[/tex] )
θ’= -13.8º
To measure this angle from the positive side of the x-axis counterclockwise.
θ = 360- θ'
θ = 360 - 13.8
θ = 346.2º
In conclusion using the expression of the magnetic force and solving the determinant we can shorten the result for the value of the force are:
Learn more here: brainly.com/question/2630590
