The expression of the magnetic force and solving the determinant allows to shorten the result for the value of the magnetic force are:
- In Cartesian form F = 2.46 i ^ - 0.605 j ^
- In the form of magnitude and direction F = 2.53 N and θ = 346.2º
Given parameters.
- Length of the wire on the z axis is: L = 25.0 cm = 0.25 m.
- The current i = 9.00 A in the positive direction of the z axis.
- The magnetic field B = (-0.242 i ^ - 0.985 j ^ -0.336 k ^ ) T
To find.
- Magnetic force.
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 <em>unit vector</em>.
Let's calculate.
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 =
F =
F = 2.53 N
Let's use trigonometry for the direction.
Tan θ ’=
θ'= tan⁻¹
θ'= tan⁻¹1 ( )
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:
- In Cartesian form F = 2.46 i ^ - 0.605 j ^
- In the form of magnitude and direction F = 2.53 N and θ = 346.2º
Learn more here: brainly.com/question/2630590