A point charge q moves with velocity v in a uniform magnetic field B. Answer the following:
a. (i) Write the vector expression for the magnetic force acting on the charge.
b. (ii) Using properties of the vector (cross) product, explain why the force is zero when v is parallel or antiparallel to B, and why its magnitude is maximum when v is perpendicular to B.
c. (iii) With the help of a suitable rule, describe how the direction of the magnetic force differs for a negative charge as compared with a positive charge moving with the same velocity in the same magnetic field.