A particle with mass m and charge q is released from the origin in a region where the electric field and magnetic field are given as B = -B₀ j and E = E₀ k . Determine the particle's speed as a function of its z -coordinate.

Step-by-step solution

By the work-energy theorem, the total work done on the particle is equal to its change in kinetic energy. The magnetic force F _m = q( v B ) is always perpendicular to the velocity vector, so the work done by the magnetic field is zero. The electric force acting on the particle is F _e = q E = q E₀ k . The work done by the electric field when the particle undergoes a displacement from the origin to a position with z -coordinate z is W_e = q E₀ z . Equating the total work done to the change in kinetic energy: W_e +