Final answer:
The magnetic force on the particle is -7.2 × 10⁻¹⁵ N in the negative j-direction (downwards). This is found by calculating the cross product of the given velocity vector and magnetic field vector.
Step-by-step explanation:
The magnetic force on a charged particle moving in a magnetic field can be calculated using the Lorentz force equation F = q(v x B), where q is the charge, v is the velocity vector and B is the magnetic field vector.
The charge of the particle is 1.0 × 10⁻¹⁹C, the velocity is given as 6.0 × 10⁴m/s i, and the magnetic field is B=(0.4i+1.2k) T. To find the magnetic force, we use the cross product of the velocity and magnetic field vectors:
F = q(v x B) = (1.0 × 10⁻¹⁹C)((6.0 × 10⁴ mi) x (0.4mi + 1.2kk))
Calculating the cross product:
mi x mi = 0, and mi x kk = -mj
F = (1.0 × 10⁻¹⁹C)((6.0 × 10⁴)(0) mi + (6.0 × 10⁴)(1.2)(-mj))
F = -7.2 × 10⁻¹⁵ N j
The direction of the force vector is in the negative j-direction, which means it is pointing downwards when using the right-hand rule with conventional current direction (positive charge).