A particle with charge $-0\mathrm{.}20$ nC moving with a speed of $6000\frac{m}{s}$ enters a region of uniform magnetic field of $0\mathrm{.}5$T$.$

a$.$ sketch the particle's path in the B$-$field. Indicate the magnetic force vectors acting on the particle at some representative positions

b$.$ Calculate the magnitude of the magnetic force

c$.$ An electric field can be applied to keep the particle moving in a straight line through the magnetic field. Calculate the magnitude of this electric field and state its direction.