Final answer:
The force in cable AB is expressed in Cartesian vector form by using the cross product of the current times length and the magnetic field vectors, represented as F2 = I21 x B1. The force per unit length can also be considered as F/1, especially when dealing with very long wires.
Step-by-step explanation:
To express the force in cable AB in Cartesian vector form, we need to consider the current I, the length of the wire l, and the magnetic field B. The force F2 on a straight current-carrying wire can be found by taking the cross product of the current times length (in unit vector notation) and the magnetic field: F2 = I21 x B1. This formula takes into account the direction and magnitude of the current and the magnetic field. To find the force per unit length, we simply use F/1. When the current vector is perpendicular to the magnetic field vector, the force is maximized since the sine of the angle between them (90 degrees) is 1.