Final answer:
The magnetic force acting on the wire is 2 A · m · T · cos(π/4)ı.
Step-by-step explanation:
The magnetic force acting on a wire carrying a current in a magnetic field is given by the formula F = I * L * B * sin(θ), where I is the current, L is the length of the wire, B is the magnetic field, and θ is the angle between the current direction and the magnetic field direction.
In this case, the wire is 2 meters long and carries a current of 5 A in the positive z direction. The magnetic field is given by B = ˆr0:2cosφ (T).
To find the magnetic force, we need to calculate the components of the magnetic field in the r and φ directions, and then use the formula to find the force.
Let's calculate the components and find the magnetic force:
B = ˆr0:2cosφ (T) = 0.2cos(π/4)ı
The magnetic force is given by:
F = I * L * B * sin(θ) = (5 A)(2 m)(0.2cos(π/4)ı)(sin(90°))
Calculating the force:
F = (5 A)(2 m)(0.2cos(π/4)ı)(1)
Simplifying the calculation:
F = 2 A · m · T · cos(π/4)ı
Therefore, the magnetic force acting on the wire is 2 A · m · T · cos(π/4)ı.