## Supplemental Problem.
Electrons are accelerated from rest through a potential difference Vo and then pass through a region between two parallel metal plates, as shown above. The region between the plates can contain a uniform electric field E and a uniform magnetic field B. With only the electric field present, the electrons follow path 1 . With only the magnetic field present, the electrons follow path 3. As drawn, the curved paths between the plates show the correct direction of deflection for each field, but not necessarily the correct path shape. With both fields present, the electrons pass undeflected along the straight path 2.
(a)
i. Which of the following describes the shape of the portion of path 1 between the plates?
___ Circular ___ Parabolic ___ Hyperbolic ___ Exponential
Justify your answer.
ii. What is the direction of the electric field?
___ To the left ___ To the top of the page ___ Into the page
___ To the right ___ To the bottom of the page ___ Out of the page
Justify your answer.
(b)
i. Which of the following describes the shape of the portion of path 3 between the plates?
___ Circular ___ Parabolic ___ Hyperbolic ___ Exponential
Justify your answer.
ii. What is the direction of the magnetic field?
___ To the left ___ To the top of the page ___ Into the page
___ To the right ___ To the bottom of the page ___ Out of the page
Justify your answer.
Between the plates the magnitude of the electric field is 3.4×104V/m, and that of the magnetic field is 2.0×10−3T.
(c) Calculate the speed of the electrons given that they are undeflected when both fields are present.
(d) Calculate the potential difference Vo required to accelerate the electrons to the speed determined in part (c).