Final Answer:
The magnetic force acting on the 2.2 m long wire is 10.9 N.
Explanation:
To determine the magnetic force acting on the wire, we need to use the formula:
F = B × I
where F is the force, B is the magnetic field strength, and I is the current flowing through the wire.
First, let’s find the magnetic field strength. The magnetic field is uniform, so we can use the equation:
B = μ₀I / 2l
where μ₀ is the permeability of free space (4π x 10^-7 T·m/A), I is the current flowing through the wire (7.2 A), and l is the length of the wire (2.2 m).
Plugging in the values, we get:
B = μ₀I / 2l = (4π x 10^-7 T·m/A) x (7.2 A) / (2.2 m) = 0.089 T
Next, we can find the x-component of the magnetic force by multiplying the magnetic field strength by the current:
Fx = B × I = 0.089 T x 7.2 A = 6.3 N
The y-component of the magnetic force can be found by using the equation:
Fy = B × I = 0.089 T x 7.2 A = 4.6 N
Finally, we add the x- and y-components to find the total magnetic force:
F = Fx + Fy = 6.3 N + 4.6 N = 10.9 N
Therefore, the magnetic force acting on the 2.2 m long wire is 10.9 N.