Question

An electron beam is passed through two charged parallel plates of length L = 20 cm and is seen to be deflected by a vertical distance d = 2.5 cm by the time it reaches the end of the plates. If the area between the plates is then filled with a uniform magnetic field B = 10-5 T pointing into the page, the electron beam is observed to be undeflected. What is the speed of the electrons?

a) 1.41x106 m/s b) 7.03x105 m/s c) 4.68x105 m/s d) 3.51x105 m/s e) 2.97x104 m/s

Answer 1

v = speed of the beam

E = electric field

B = magnetic field

forthe beam to pass undeflected

F_e = F_b

qE = qvB

E = Bv                      eq-1

acceleration due to electric field is given as

a = qE/m

time taken to cross the plates is given as

t = L/v

along the vertical direction

d = (0.5) a t²

d = (0.5) (qE/m) ( L/v)²

d = (0.5) (qBv/m) ( L/v)²

0.025 = (0.5) ((1.6 x 10^-19) (10^-5) v/(9.1 x 10^-31)) ( 0.20/v)²

v = 1.41 x 10⁶ m/s