Please show all work and eqautions needed to find the answer in red In the figur

Question

Please show all work and eqautions needed to find the answer in red

In the figure, an electron is accelerated through a potential difference V_1 so that it is moving in the +x direction when it enters the gap between two large parallel plates. The two parallel plates have separation d = 0.03 m and potential difference V_2 = 120 V. The lower plate is at the lower potential. A uniform magnetic field of magnitude 0.5 T is setup between the plates so that the electron travels in a straight line. Neglect fringing and assume that the magnetic field is perpendicular to the electron's velocity. a. What is the direction of the magnetic field between the plates? The coordinate system is shown in the figure. i. +y direction ii. -y direction iii. +z direction iv. -z direction b. What is the velocity of the electron?

Explanation / Answer

a) since the electron travels straight line ,and it was acted by two fields,then the forces due to electric and magnetic fields are balanced

the direction of electric force is in upward direction ,to balnce this the magnetic force must be in downward direction

to get a downward magnetic force ,the field should be in -z-direction

b) Electric force = magnetic force

q*E = q*v*B

E = v*B

velocity v = E/B = (V/d)/B = (120/0.03)/0.5 = 8000m/s

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