Useful Constants with Equation Sheets

Physics 212FinalFall 2001

NAME:______MC

Useful Constants with equation sheets

Part I: Multiple Choice (4 points. ea.) READ EACH QUESTION CAREFULLY!

Choose the best answer

___ 1. When two circuits are linked via a mutual inductance, then

(A)the mutual inductance which links circuit one to circuit two is greater than the mutual inductance which links circuit two to circuit one if circuit one’s coils has more turns.

(B)the mutual inductance depends only the EMF and how fast the current changes.

(C)a steady current in one circuit produces an EMF in the other.

(D) all of the above.

(E)none of the above.

___ 2. An ideal series R-L-C circuit (under damped) is connected to a switch. The capacitor is initially charged when the switch is closed at t=0. Which graph below best describes the voltage across the capacitor as a function of time? /
(A) / / (C) /
(B) / / (D) / / (E) none of the above.
___ 4. A current i goes through an ideal inductor as shown at right. If the current is decreasing, then
(A) the potential at (a) is higher than at (b).
(B) the potential at (a) is the same as that than at (b).
(C) the potential at (a) is lower than at (b).
(D) the potential at (a) is independent of the potential at (b).
(E) none of the above. /

___ 5. In a given series R-L-C circuit operated at some fixed frequency, if the inductance were to be decreased, then

(A) the impedance of the series combination would decrease.

(B) the impedance of the series combination would increase.

(D) the impedance of the series combination could increase, decrease or remain the same depending upon the actual change in inductance.

(E) the impedance of the series combination would necessarily be zero.

____ 6. In a series R-L-C circuit operated at some fixed frequency, the phase of the current in the capacitor

(A) lags the phase of the current in the resistor by 90º.

(B) lags the phase of the current in the inductor by 180º.

(D) leads the phase of the current in the resistor by 180º.

(E) is in phase with the current of both the inductor and the resistor.

____ 7. A step-up transformer, such as the one used in the often demonstrated Jacob’s Ladder,

(A) “steps up” the voltage power at the secondary compared to that at the primary.

(B) “steps down” the current at the secondary compared to that at the primary.

(D) all of the above.

(E) none of the above.

___ 8. Electromagnetic waves in vacuum

(A) travel at a speed which is independent the frequency of the waves.

(B) are consistent with Maxwell's equations.

(D) carry momentum.

(E) all of the above.

___ 9. The energy stored in an electromagnetic wave

(A) is split evenly between the electric and magnetic fields.

(B) is stored entirely in the magnetic field.

(D) is 0, energy cannot be stored in mathematical abstractions.

___ 10. In electromagnetic radiation, the Poynting vector

(A) is perpendicular to B, the magnetic field.

(B) is perpendicular to E, the electric field.

(D) has average magnitude equal to the radiation intensity.

(E) all of the above.

___ 11. Electric charge is conserved

(A)always.

(B)never.

(C)only in conductors.

(D)except within conductors.

(E)electric charge conservation was never discussed in this class.

___ 12. Gauss's law

(A) relates the total electric flux through a closed surface with the net electric charge enclosed within the surface.

(B) is completely equivalent to the inverse square law for the electric field due to a point charge.

(D) is very useful for charge configurations with symmetry.

(E) all of the above.

___ 13. A conductor is a material in which, under static conditions,

(A) there are charges which are free to move.

(B) the electric field is always zero.

(D) all of the above.

(E) none of the above.

___ 14. Relative to the gravitational attraction between two protons, the electrostatic repulsion is

(A) much larger.

(B) about the same.

(D) trick question since the gravitational force will be repulsive, not attractive.

(E) zero between the same kinds of particles.

___ 15. The dielectric strength for a material is

(A) the factor by which the capacitance increases when the material is inserted between the plates of a parallel plate capacitor.

(B) the factor by which the magnitude of the electric field decreases when the material is inserted between the plates of a parallel plate capacitor.

(C) the factor by which the potential decreases when the material is inserted between the plates of a parallel plate capacitor.

(D) the maximum electric field the material can withstand before dielectric breakdown.

(E) (A) through (C) the above.

___ 16. The effective capacitance of two capacitors connected in series is

(A) always less than the individual capacitance of either of the two capacitors.

(B) always greater than the individual capacitance of either of the two capacitors.

(D) always less than the individual capacitance of either of the two capacitors.

(E) none of the above always holds.

___ 17. The principles used to derive Kirchoff’s rules for electric circuit analysis were

(A) conservation of energy and conservation of momentum.

(B) conservation of energy and conservation of charge.

(D) symmetry and conservation of energy.

(E) no principles are required as the necessary equations can be found in the chapter summary.

___ 18. A negative charge moves south through a magnetic field directed to the west. The particle will be deflected

(A)North.

(B)Up.

(C)Down.

(D) East.

(E)not at all.

___ 19. The magnetic field of a long straight wire carrying a current out of the page has field lines given by

(A) / (B)
(C) / (D)

(E) There is no magnetic field unless the current is changing.

___ 20. Lenz's Law, which describes induced currents and EMF’s as a resistance to change in magnetic flux, was described by Dr. Gallis as

(A) electromagnetic friction.

(B) electromagnetic inertia.

(D) electromagnetic hocus pocus.

Part II Problems(15 points each)

Show all work. No work = no credit!

1.) Self inductance of a coaxial cable: A small solid conductor with radius a is supported by insulating disks on the axis of a thin walled tube with inner radius b. The inner and outer conductors carry equal currents i in opposite directions. From work done with Ampere’s Law earlier this semester, we know that in the region between the two conductors the magnetic field strength is given by

a) Write the expression for the flux dB through a narrow strip of length l and width dr, parallel to the axis and a distance r from the inner conductor lying in a plane containing the axis of the coaxial cable. /
b) Integrate your expression to find the total flux produced in the region between the conductors.
c) From the last result, derive an expression for the inductance L of a length l of coaxial cable. The result should be expressed in terms of the variables a, b, andl, as well as 0. /

2) You are asked to design an L-C circuit in which the stored energy is 3.00x10-4 J and the natural frequency is 0 = 3.00x104 rad/s. Because of the limited dielectric strength of the material used in the capacitor, the maximum voltage across it is to be 50.0 V.

(A) Determine the capacitance required, knowing that the voltage across the capacitance will be a maximum at the same points in time when all the energy in the circuit is stored in the capacitor.

(B) Determine the inductance of the inductor given the natural frequency and the capacitance determined in part (A).

3. An L-R-C series circuit is constructed with a 2.00 H inductor, two resistors in series (R1 =50 R2 =150 ), and a 8.00 F capacitor. Determine

(A) the resonant frequency (in rad/s) of this circuit,
(B) the effective resistance of the two resistors in series.
If the circuit is driven by a 4.00 V (amplitude) source with a frequency of 200 rad/s, calculate the
(C) inductive reactance of the inductor,
(D) capacitive reactance of the capacitor,
(E) impedance of the entire series combination,
(F) the current amplitude for the current through the combination,
(G) the phase angle for the current relative to the voltage,
(H) the voltage amplitude for the capacitor,
(I) the voltage amplitude for the inductor,
(J) the voltage amplitude for the resistor R2,
(K) the impedance of just the series combination of the inductor and R1,
(L) the voltage amplitude across just the series combination of the inductor and R1. /

4. A monochromatic light source with power output 100 W radiates light of wavelength 500nm uniformly in all directions. At a distance of 4.00 m, determine

(A) the frequency (in Hz) of the light,

(B) the intensity of the light,

(D) the magnetic field amplitude,

(E) the average energy density associated with the light.

(F) What is the force exerted by the light on a mirror (ideal reflector) 2cm x 4cm if it is used to reflect the beam back upon itself?

(G) What is the force exerted by the light on a 1cm x 1cm flat black material?

5. An alpha particle (mass of 4 u, charge of +2e) is accelerated from rest across a potential difference of 10 million Volts.

a) What is the kinetic energy (in Joules) of the alpha particle as it leaves the accelerator?

b) What is the speed of the alpha particle ?

The alpha particle now makes a head on “collision” (approaching from “very far away”) with a gold nucleus (which has atomic number 79, and hence a charge of +79e). Assume the nucleus is stationary for this problem.

c) What is the speed of the alpha particle at the turn around point?

d) What is the kinetic energy of the alpha particle at the turn around point?

e) What is the potential energy of the alpha particle at the turn around point?

f) What is the distance between the alpha particle and the nucleus at the turn around point?

6) In the figure shown at right, use Kirchoff’s laws to determine
(A) the unknown current I,
(B) the unknown emf E, and the
(C) the unknown resistance r. /
7) For the diagram shown below
a) Calculate the equivalent capacitance of the capacitor network.
b) Calculate the charge on each capacitor, the potential difference across each capacitor. /

8) Charges are accelerated by an accelerating potential of 50 kV (of appropriate polarity for positive or negative charges) into a region of uniform magnetic field (directed out of the page).

If the charges are electrons,
(A) What is the speed of the electrons as they enter the magnetic field?
(B) Indicate the path of the electrons on the diagram at right (label the path e).
(C) What is the radius of the circular path taken by the electrons as they travel in the uniform magnetic field?
If the charges are protons:
(D) What is the speed of the protons as they enter the magnetic field?
(E) Indicate the path of the protons on the diagram at right (label the path p).
(F) What is the radius of the circular path taken by the protons as they travel in the uniform magnetic field? /

Bonus: 2 points each:

(A) .

(B) .

(D) .

(E) .

For the Equations above

___ 1. Which of the equations is the Lorentz Force Law?

___ 2. Which two of the equations show how changing fields can create new fields, allowing the propagation of electromagnetic waves even when there are no source charges or currents?

Scratch Paper Page

Useful Constants:
k= 9.0 x109 Nm2/C2
= 8.85 x 10-12 C2/(N m2)
e= 1.6 x 10-19 C
me= 9.1 x 10-31 kg
mp= 1.67 x 10-27 kg
1 eV = 1.6x10-19 J
g= 9.8 m/s2
= 4 x 10-7 N s2/C2
c= 3.00 x 108m/s
1u= 1.66 x 10-27 kg /