SCI 113 PHYSICS – THEORY AND EXPERIMENT
THINGS TO KNOW FOR THE FINAL EXAM
FALL 2013
(there will be 10 regular and 2 bonus problems at the final)
Ch. 15. 15.1, 15.3, 15.4, 15.5, 15.9
You should know Coulomb’s law, the definition of the electric field, the principle of
superposition for electric fields (remember that they sum up as vectors). You should
know and understand the definition of electric flux  E (and in general, the flux of any
vector field through a surface) and be able to calculate it in simple cases. You should
understand and be able to use Gauss’s law.
Ch. 19. 19.1, 19.2, 19.3, 19.4, 19.6, 19.7
You should understand and be able to use the formula for the Lorentz force. Remember,
that the Lorentz force is always perpendicular to the velocity and therefore it changes
only the direction of the velocity and not its magnitude. (Does the kinetic energy of a
particle moving in a static magnetic field change?) Using the Lorentz force you should be
able to explain qualitatively the force on a current carrying wire in a magnetic field
(electric motor) and also to explain qualitatively the induced current when you move a
wire across a magnetic field (electric generator).You should know how the magnetic field
around a straight wire with current depends on the distance to the wire and on the current.
You should understand and be able to use Ampere’s law and know and understand how
the “Circulation of the magnetic field around a loop” (and in general, the circulation of
any vector field along a curve) is defined. You should be able to calculate directly from
the definition this circulation in simple cases.
Ch. 20. 20.1, 20.3, 21.8, 21.11
You should understand Faraday’s law and know the definition of emf =”Circulation of
the electric field around a loop” as well as know the definition of the magnetic flux
 m through a surface. Remember that there are two different cases when one considers
induction– when the loop is moving across the magnetic field, you can use the Lorentz
force to explain the induced current. But if the loop is stationary and the magnetic field is
changing, then this changing magnetic field produces (circular) electric field. Remember
the Maxwell addition to the laws of electromagnetism – “changing electric field can also
produce (circular) magnetic field”.
You should understand and be able to use the four Maxwell equations.
Ch. 26. 26.1, 26.2, 26.3, 26.4, 26.5, 26.7, 26.8
You should understand the problem with simultaneity. Remember that two events,
happening at different places, can look in reverse order to two different observers,
moving relative to each other. Time dilation and length contraction. You should know the
corresponding formulas. You should understand “The twin paradox”. Remember that the
twin that makes the space trip does indeed come back younger. Why isn’t there an actual
paradox? Answer – the twin who made the space trip moved in a noninertial system
which is not equivalent to the system connected with the earth.
You should understand the formulas for the relativistic mass, momentum and energy and
be able to apply them. Should know and understand Einstein’s equivalence principle.
Ch. 27. 27.2
Understand the details of the photoelectric effect and Einstein’s formula for the energy of
the photons.
Problem 1.
Electric current of 0.3 A along a wire creates circular magnetic field. A loop  in the
shape of a square with side 0.1 m surrounds the wire as shown. What is the circulation of
the magnetic field along  (with respect to the orientation indicated) in case a) and b)?
a)
b)
I
I


Problem 2.
How fast must a particle travel relative to an observer for its kinetic energy to be three
times its rest-mass energy?
Problem 3.
Under what conditions is the velocity of a charged particle conserved when it is moving
in some steady magnetic field? Under what conditions is its speed conserved?
(Remember how the Lorentz force acts.)
Problem 4.
Describe “the twin paradox. Why is it called a paradox? Is there really a paradox?
Problem 5.
Suppose you have magnetic field, which is zero in the lower half-space and is nonzero,
homogeneous, horizontal in the upper half-space with magnitude B =0.5 T. What is the

Circulation of B around the curve, indicated? (The curve is a square with sides 10 cm,
the orientation is counterclockwise.)

B
Problem 6.
Indicate which of the following statements are correct:
If you could run with a constant speed close to the speed of light (relative to your friend)
a) you would look slimmer to your friend, due to length contraction
b) you would look smaller to your friend due to contraction of all your dimensions
c) your friend would look fatter to you, because you are contracted
Problem 8.
You have a rectangular loop of wire, one side of which is interrupted by a voltmeter. The
sides of the rectangle are 0.6m and 0.4 m. The loop is in a place where there is uniform
magnetic field B=0.2 T, at an angle 450 to the plane of the loop. What will be the average
voltage measured by the voltmeter (the e.m.f.) if the magnetic field reverses its direction
in 1.5 s?

B
V
Problem 9.
Find the direction and magnitude of the electric field in the middle point between two
point-like charges, which are 1 m apart. One of the charges is positive, Q1=+5 C, the
other is negative, Q2= -3C.
Problem 10.
In our derivation of time dilation we used a very special type of clock, utilizing light
pulses, to show that the moving clock must “tic” slower than the one at rest with respect
to us. How do we know that any other type of clock should slow down in exactly the
same way?
Problem 11.
A spaceship moves with a speed v  0.9c relative to a space platform that has a landing
strip 5000 m long. What is the apparent length of the landing strip as measured in the
frame of the spaceship?
Problem 14.
A circle  is in a region, where there is homogeneous magnetic field B =0.5 T. The
circle has radius 20 cm and its plane is perpendicular to the magnetic field. Find the
circulation Circ  B of the magnetic field around  and the magnetic flux  m through
the surface, spanned on the circle.

B

Problem 15.
Trough which surface is the (outward) flux of the electric field maximal – the sphere or
the cube or is it equal through both? (Note that two of the charges are positive, the third is
negative.)
+3C
- 2C
+2C
Problem 16.
When you shine blue light with wavelength 450  10 9 m on one of the electrodes of a
photocell, a current starts flowing due to the photoelectric effect. When you apply some
retarding voltage this current stops. Estimate the minimal value of this voltage Uc ,
necessary to stop the current, if the work function (separation energy for separating the
electron from the surface of the metal) is 2 eV
Problem 17.
Given that some metal has work function 2.5 eV, find the maximal wavelength of light
that can cause photoelectric effect for this metal.
Bonus problem (10 pt).
Your twin-brother is moving in a spaceship with very high speed v (towards you or away
from you) and is sending to you electromagnetic pulses each second, according to his
clock. Is it possible for you to receive his signals at intervals 0.5 s? If yes, with what
speed and in which direction must your brother be moving?
Bonus problem (20 pt).
a) Use one of the fundamental laws of electricity to find the connection between the
charge on one of the two plates of a capacitor, consisting of two large flat oppositely
charged plates, and the electric field between the plates.
b) Using part (a), try to do what Maxwell did – show that Ampere’s law by itself is
inconsistent and that the second term in the last Maxwell equation is precisely what is
needed to make the equation consistent. (Hint: Consider a wire with current, charging
a capacitor. Choose appropriately two different surfaces, spanned on the loop  .)
Bonus problem (15 points).
Derive the relativistic correction factor from the amount of slowing down of a moving
optical clock (using optical pulses traveling up and down). Does all other clocks slow
down by the same factor? Why?
Bonus problem (20 points).
Find the attractive electric force between two large parallel metal plates (in vacuum), the
voltage between which is 400 V. Both plates have area 1 m2. The distance between the
plates is 0.01 m.
Formulas:
Electricity and magnetism:
Q
e 
(The total electric flux through a closed surface)
0
 m = 0 (The total magnetic flux through a closed surface)


 m
Circ  E =e.m.f.= 
(The circulation of E around the loop  - Faraday’s law)
t


 e
Circ  B   0 I   0 0
(The circulation of B around the loop  - Ampère’s law
t
and Maxwell’s addition)
B
0I
2r
(Magnetic field around a straight long wire with current I - Biot-Savart)
F  qvB sin  (Magnitude of the Lorentz force)
Relativity:
relativistic correction factor:  
1
1
v2
c2
,
relativistic mass: m 
m0
1
relativistic kinetic energy: KE  mc 2  m 0 c 2 , total energy: E  mc 2 ,
rest-mass energy: E0  m0 c 2
Energy of the photon Einstein’s formula: E  hf
Constants:
v2
c2
 0  8.85  10 12 C2 . N-1 . m-2 (electric) permittivity of vacuum
k
1
4 0
 9  10 9 N  m 2  C -2 Coulomb constant
 0  4  10 7 N . A-2
e  1.6  10 19 C
(magnetic) permeability of vacuum
charge of the electron
h  6.6  10 34 J.s Planck’s constant
m e  9.1 10 31 kg mass of electron