NO QUESTIONS DURING THE EXAM !
PHYS 102 – Midterm – April, 2 2019
Section Number
Name&Surname:............................................................
Student number: ............................................................
Read carefully before you start: The exam is 80 minutes. Mobile phones, calculators and pocket computers are not
allowed. Show clearly how you obtain your results.
Writing Missing information about name, last name, section number will end up in a loss of 5 points.
𝑞
r
𝑟
dE⃑ = k
dq
r
r
E⃑ = k
𝐸=−
𝑑𝑉
𝑑𝑟
𝐹=−
𝑑𝑈
𝑑𝑟
𝐶=𝜀
𝐴
𝑑
𝜙=
𝐸⃑ ∙ 𝑑𝐴⃗ =
𝐹⃑ = 𝑞𝐸⃑
𝜙=
𝐹⃑ = 𝑘
𝐸⃑ ∙ 𝑑𝐴⃗
𝑞
𝜀
𝑄 = 𝜌𝑉
𝐸=
𝑞 𝑞
𝑟̂
𝑟
𝜎
2𝜀
𝑄 = 𝜎𝐴
∆𝑉 = −
𝐸⃑ ∙ 𝑑𝑙⃗
𝑉=
𝑞
𝑟
∆𝑈 = 𝑞∆𝑉
𝑄 = 𝜆𝑙
𝑑𝑄 = 𝜌𝑑𝑉
𝑉=𝑘
1) (25 points) For the system given in the figure
a) What is the net electric field 𝐸⃑ at point P which is located at (3a,0)?
b) What is the electric potential at point P?
c) How much work has to be done to bring a third charge +q from infinity to point P?
d) After +q is brought from infinity to point P, what is the net electric force 𝐹⃑ acting on +q?
(Provide your answers in terms of k,q,a)
𝑘
𝑑𝑞
𝑟
𝑊 = ∆𝑈
𝑈=𝑘
𝑞 𝑞
𝑟
𝑄 = 𝐶∆𝑉
𝑑𝑄 = 𝜆𝑑𝑙 𝑑𝑄 = 𝜎𝑑𝐴
NO QUESTIONS DURING THE EXAM !
2) (25 points) An insulating solid sphere with radius 𝑟 = 2𝑎 carries a total charge of 𝑄 uniformly distributed to its
volume. This solid sphere placed in the center region of a conducting spherical shell with inner radius 𝑟 = 3𝑎 and outer
radius 𝑟 = 5𝑎. The conductor carries a total charge of −4𝑄.
a)
b)
c)
d)
e)
f)
Draw the electrical field lines everywhere.
Calculate the electrical field at radial distance 𝑟 = 𝑎 .
What is the charge on the inner surface of the conductor?
What is the charge on the outer surface of the conductor?
What is the electric field at 𝑟 = 4𝑎?
Calculate the electrical field at radial distance 𝑟 = 8𝑎 .
(Provide your answers in terms of k,Q,a)
NO QUESTIONS DURING THE EXAM !
Name&Surname:...............................................
Student number: ............................................. Section…………….
3) (25 points) A thin rod of length L is placed on the x-axis as shown in the figure so that it is centered at the origin. The
rod carries uniform charge 𝟐𝑸 along its length.
a) Determine the electric potential at point A.
b) Determine the electric field vector at point A.
(Provide your answers in terms of k,Q,L)
NO QUESTIONS DURING THE EXAM !
4) (25 points) Two identical conducting plates with area 𝐴 are carrying charges −𝑄 and 𝑄 and separated by a very small
distance 𝑑 as shown in the figure on the right. Electric field only exists between the plates
𝑄
with a magnitude of 𝐸 = 𝜎 𝜀0 = 𝐴𝜀
0
a) Show the direction of the electric field and express the electric field between the
plates using unit vector notation.
b) Determine the electric potential difference between the plates. Please DO NOT
just write the answer. You need to show how you obtained that answer.
c) What is the capacitance of this parallel plate capacitor?
(Provide your answers in terms of A, 𝜎,Q,d,𝜀 )