A beam of protons is directed in a straight line along the +z direction through a region of space in which there are crossed electric and magnetic fields. If the electric field is 800 V/m in the −y direction and the protons move at a constant speed of 105 m/s, what must be the magnitude and direction of the magnetic field such that the beam of protons continues along its straight-line trajectory? magnitude .008 Correct: Your answer is correct. T direction

B = 7.6 T   direction of + x

Explanation:

For the proton beam to continue in the same direction the electric and magnetic forces must be equal

              = 0

              = F_{e}

              Fm = q E

The electric force is in the direction of the electric field because it is the charge of the positive proton, the electric force goes in the direction of –y, therefore, the magnetic force cancels this force must go in the direction of + y

 The magnetic force is

             F_{m} = q v x B = q v B sin θ

             θ = 90

             B = q E / q v

             B = E / v

             B = 800/105

             B = 7.6 T

To find the direction of the magnetic field we use the right hand rule, the thumb goes in the direction of the proton velocity, the fingers extended in the direction of the magnetic field and the palm is the direction of force, for a positive charge.

Thumb goes in the direction of the + z axis

Palm in the direction of +y

Fingers point in the direction of + x