Question

At a particular instant, a proton moves toward the east in a uniform magnetic field that is directed straight downward. The magnetic force that acts on it is

Answer 1

Solution) Proton has positive charge q

You can assume coordinate system where you can compare positive X axis to east ( + i) vectorially , similarly positive Y axis as North (+ j ) , negative Y or down is South (- j) and negative X is west ( - i ).

It's velocity now moving east so it's direction is along (+ i ) = V(i)

Since magnetic field is directed straight downward so it's direction is ( - j ) = B( - j )

Magnetic force F is given by

F = qV(i) × B(- j )

F = BqV( i × (- j)) = - BqV( i × j )

We have i × j = k in vectors

F = - BqV(k)

F = BqV( - k )

Here ( - k ) indicates direction is inwards or into

So magnetic force is into .