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Exam #2, Electrostatics
Prof. Maurik Holtrop Department of Physics PHYS 408 University of New Hampshire March 27th, 2003
Name: _________________________ Student # ____________________
Problem Description Available Points Score
I Electron at origin 20
II Dipole in E field 20
III Parallel metal plates 20
IV Spherical Shells 20
V Charged semi circle 20
NOTE: There are 5 questions. You have until 9 pm to finish. You must staple your “Formula-sheet” to the back of this exam when handing it in. You are allowed to use your calculator.
Work out all problems using variables, then put in numbers. Partial credit can
only be given to clearly worked out problems.
Useful information:
9 2 0
8.99 10 Nm C 4
k
= = × -
Speed of light: c = 3x 10
12 2 -1 -
ε 0 8.85 10 C N m
= × −
1 eV = 1.60 × 10 −^19 J
e = 1.60 × 10 −^19 C
(^8) m/s 1 MeV = 10 (^6) eV
Mass of an electron: Me = 0.5 MeV/c^2 Mass of a proton (approx.): Mp=1000MeV/c^2
I) Note: In this problem express all your answers in terms of the relevant variables, i.e. use e , r, d and constants. A single electron is placed at the origin.
a) What is the equation for the electric vector field due to this electron at a distance r from the origin?
b) What is the equation for the electric potential due to this electron at a distance r from the origin?
c) A second electron is now brought “from infinity” and placed on the x axis at x=d. What is the force (magnitude and direction) on this second electron due to the first?
d) (See part c.) What is the amount of work that needs to be done to place this second electron?
V= +500V V= -500V
d
III) Two “infinite” metal plates in the z-y plane are separated by a distance, d, of 5 cm. The left plate is held at a potential of Vleft= +500V and located at x=-2.5cm, the right plate is located at x= +2.5cm and held at a potential of Vright= -500V.
a) Draw the electric field lines, indicating the direction of the field with arrows. Also draw the equipotential surfaces as dashed lines.
b) If a proton is released right at the surface of the left plate, what is the velocity of this proton when it hits the right plate? (express your answer in terms of the speed of light, c , ignore gravity)
c) What would be the equation for the potential anywhere between the plates? (Hint: this means, V(x) = some function of x)
d) Using the result from c, what is the electric field anywhere between the plates?
e) What is the surface charge density on each of the plates? (Hint: Use the result you get for the electric field from Gauss’ law and from part d)
V) A section of a thin plastic circle with radius R spans an arc of π radians. It has a charge Q uniformly distributed on it. For the point C in the center of this circle:
y
dq
A) Draw the vector for the contribution to the E
G
field of the small charge element dq in the picture, label this Edq , also draw the vector E
G
field due to the total charge Q, label this Etot.
R
C
x
B) Setup the equation for the contribution to the E
G
field at point C due to the small charge element dq on the circle.
C) Setup the integral for the E
G
field at point C, including the limits.
D) Calculate the electric field at point C. Express your answer in terms of Q and R.
