At a given moment the particle is moving in the +x direction (and the magnetic field is always in the +z direction). If qqq is positive, what is the direction of the force on the particle due to the magnetic field?

Therefore, the force exerted by the magnetic field on the particle goes along the positive y- direction

Explanation:

The equation for the force exerted on a particle due to the magnetic field is equal to:

F = q*(v * B)

If we replace vi for v, +q for q and -Bk for B, we have:

F = +q*(vi*(-Bk)) = -q*v*B*(i * k)

From this equation we have that the vector i is in direction -x and k in direction -z

We compute the cross product of two unit vectors:

i * k = -j, where j is the vector along -y direction

Replacing we have:

F = -q*v*B*(-j) = -q*v*B*j

Therefore, the force exerted by the magnetic field on the particle goes along the positive y- direction