Assignment:
Problem 1. A parallel plate capacitor is constructed of two conducting plates spaced a distance d = 3.00 mm apart. It is charged to a potential difference of 500 Volts. A proton (mass 1.67 x 10-27 kg) is shot through a small hole in the negative plate with an initial speed vi = 2.00 x 105 m/s.
(a) On the diagram, Sketch and label the "source" electric charges on the parallel plates.
(b) Sketch and label 4 electric field lines in the capacitor (between the conducting plates). Ignore fringe effects.
(c) Sketch and label equipotentials for 100 V, 200 V, 300 V, 400 V. Use your ruler to space these lines properly! Careful artwork is important here!
(d) What is the total energy of the proton when it enters the capacitor?
(e) What is the electric potential energy of the proton as it passes the 200 V equipotential surface?
(f) Using energy conservation, calculate the kinetic energy of the proton as it passes the 200 V equipotential surface.
(g) Will the proton make it to the 500 V plate or will it momentarily stop and reverse direction before reaching the 500 V plate? A numerical calculation is required to support your answer.
(h) If the proton momentarily stops and reverses direction before reaching the 500 V plate, calculate the maximum distance from the 0 V plate it travels before doing so.
(i) What is the acceleration of the proton while it is travelling between the plates?
(j) Is the acceleration you calculated in part (i) constant while the proton travels between the plates? If so, WHY?
(k) If the proton momentarily stops and reverses direction before reaching the 500 V plate, calculate the time it takes to momentarily come to rest.
Problem 2. Consider a proton (mass = 1.67 x 10 -27 kg, qproton= +e) in the potential field of an iron nucleus (mass = 9.40 x 10-26 kg, qiron= + 26e). Three equipotential surfaces are shown in the diagram as dashed circles; the equipotential lines are NOT equally spaced. Treat the iron nucleus as a point charge.
a) Calculate the radial distance from the iron nucleus at which the electric potential is 5.00 Volts.
b) Calculate the radial distance from the iron nucleus at which the electric potential is 3.00 Volts.
c) Calculate the radial distance from the iron nucleus at which the electric potential is 1.00 Volts.
d) Sketch and label 8 electric field lines for the iron nucleus. HINT: What is the relationship between the equipotential surfaces and electric field lines?
e) Suppose we now put a proton, initially at rest, at the inner equipotential. What is the speed of the proton when it reaches the outer equipotential? Hint: Use energy conservation!
f) Could you use the equations for uniformly accelerated motion from College Physics I (for example, those shown below) to solve part e)? Why or why not?
vxf = vx.i + axt
V2x,f - v2x,i + 2ax (xf - Xi)