Final answer:
The magnitude of the force exerted on the wire is 0.6957 N, and the direction is downwards along the negative y-axis, as determined by the right-hand rule.
Step-by-step explanation:
To find the magnitude and direction of the force exerted on a wire carrying a current in a magnetic field, we use the equation for the magnetic force on a current-carrying wire: F = I * L * B * sin(θ), where F is the force in newtons, I is the current in amperes, L is the length of the wire in the magnetic field in meters, B is the magnetic field strength in teslas, and θ is the angle between the current direction and the magnetic field direction.
In this case, since the current is in the z direction and the magnetic field is in the x direction, the angle θ is 90 degrees, and sin(θ) is equal to 1. Thus, the force exerted on the wire is:
F = (4.9 A) * (0.33 m) * (0.43 T) * sin(90 degrees)
Since sin(90 degrees) is 1, we can simplify this to:
F = 4.9 A * 0.33 m * 0.43 T
Which gives us:
F = 0.6957 N
The direction of the force is determined by the right-hand rule. Since the current is in the positive z direction and the magnetic field is in the positive x direction, the force will be in the negative y direction or downwards when looking from the positive z-axis towards the origin.