Question

A particle with positive charge q = 9.61 10-19 C moves with a velocity v = (3î + 4ĵ − k) m/s through a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total force on the moving particle, taking B = (4î + 3ĵ + k) T and E = (3î − ĵ − 4k) V/m. (Give your answers in N for each component.) Fx = N Fy = N Fz = N (b) What angle does the force vector make with the positive x-axis? (Give your answer in degrees counterclockwise from the +x-axis.) ° counterclockwise from the +x-axis (c) What If? For what vector electric field would the total force on the particle be zero? (Give your answers in V/m for each component.) Ex = V/m Ey = V/m Ez = V/m

Answer 1

We know that in force F_e due to electric field on charge is given by

So

  

Now the force due to magnetic field is given by F_b

So the resultant force F_t is given by

Now Angle made with x axis by a vector A_xi+A_yj+A_zk

C) Now we are given just magnetic field, therefore magnetic force, and we need to find electric force for which net force is 0;

Now let electric field be E then,

So now F_t is given by,

(According to condition)