Final answer:
The size of the magnetic force on a wire in a magnetic field can be determined using the formula F = ILBsin(θ), which simplifies to F = ILB when the current and magnetic field are perpendicular. The forces on the sides of a rectangular loop in a magnetic field can cancel out when the plane of the loop is perpendicular to the field. The magnetic force on a wire segment allows calculation of the magnetic field using B = F / (IL).
Step-by-step explanation:
To determine the size of the magnetic force on a wire due to an applied magnetic field, we use the formula F = ILBsin(θ), where F is the magnetic force on the wire, I is the current flowing through the wire, L is the length of the wire within the magnetic field, B is the magnetic field strength, and θ is the angle between the direction of the current and the direction of the magnetic field. Assuming a current I, a wire length L, and a magnetic field B with θ being 90 degrees (current and field are perpendicular), the formula simplifies to F = ILB.
For a rectangular loop of wire in a uniform magnetic field, when the plane of the loop is perpendicular to the magnetic field, the forces on the sides parallel to the field cancel each other out, and there is no resultant force on the loop (assuming the loop is entirely within the field). This is because the force on one side will be in the opposite direction to the force on the adjacent side, due to the direction of current being reversed in the second side.
Also, using the magnetic force formula for a straight wire segment, given a current of 0.40 A and a magnetic force of 0.022 N exerted on a 10 cm wire segment, we would solve for B. With these values plugged into the magnetic force formula F = ILB (and converting cm to meters), we get B = F / (IL).