Name:
Sample Exam A
Activity ID:
Problem 2. Rutherford’s 1st model of the atom had a positive point charge (+Ze) at the
centre of a sphere of radius R with a uniformly distributed negative charge (-Ze) throughout
the entire volume. Consider instead a doubly ionized atom so there are now only (Z-2)
electrons.
~ everywhere in space ( i.e. r < R, and r > R ).
a) Calculate the Electric field E
b) Calculate the electric potential everywhere in space assuming V = 0 at r = 1.
4
Name:
Activity ID:
Problem 3. A rectangular loop of wire 2.0m⇥4.0m is placed in the xy-plane with a spatially
uniform magnetic field at 30 as shown. The spatially uniform magnetic field depends on
time according to B(t) = B0 (1 at) where B0 = 0.50 T and a = 0.5 s 1 . At t=1s, the
loop is located 1m in the spatially uniform magnetic field and moving with a speed of 2
m/s into the field region. Calculate the magnitude and direction of the induced current in
the wire at t = 1s.
Loop
B
Loop
B
30
Side view
Top view
5
Name:
Activity ID:
Problem 4. A simple optical filter can be constructed from a thin film of titanium dioxide
deposited on optical glass. The refractive index of the glass is nglass = 1.53 and titanium
dioxide nf ilm = 2.68. Assume normal incidence for the light rays.
a) If the wavelengths of light maximally reflected by the filter are 1 = 690 nm (red), and
2 = 414 nm (violet), find the minimum thickness of the thin film.
b) Now suppose that the thickness of the thin film t = 250 nm. What wavelength of
visible light is preferentially transmitted by this optical filter? (HINT– if an incident wave
is preferentially transmitted, what must be true of its reflected waves?)
6
Name:
Activity ID:
Problem 5. All currents are 0 when the switch S is closed at t = 0 in the circuit shown.
d
a) Calculate the potential di↵erences Vab and Vde at t = 0.
a
S1
R2
L
E
b) Which point, a or b, is at the higher potential?
b
e
c) Find the currents through R1 and R2 at t = 0.
R1
C
c
After a very long time, the switch is opened.
R0
d) Find the potential di↵erences Vab and Vde just after the switch is opened.
e) Find the currents through R1 and R2 just after the switch is opened.
7
f
Name:
Activity ID:
Problem 6. The RLC circuit shown below contains 2 identical capacitors and two switches
S1 and S2 . The AC power supply has a maximum voltage = 12V and a driving frequency
= 60 Hz. When both switches are open the current is ahead of the voltage by 30.9 , when
only S1 is closed the current is behind the voltage by 15.0 . If we close both switches the
current has a maximum amplitude = 447 mA. Calculate the values of R, C, and L.
8
Name:
Activity ID:
Problem 7. Computer memory in old computers such as those on the Space Shuttle were
made from loops of wire and information was stored in the magnetic field. Part of such a
memory unit was made from a very long thin insulated wire carrying a current I which is
bent into the shape shown below with a circular arc of radius R at the point C.
I
C
a) Calculate the magnitude and direction of the magnetic
D
I
field at the centre of the circular section C.
P
b) If the circular section is rotated 90 about the line between P and C so that point D is
out of the page, find the magnetic field at C.
9
I