PHYS4210 Electromagnetic Theory Quiz 1 Feb 2010

Transcription

1 PHYS4210 Electromagnetic Theory Quiz 1 Feb An electric dipole is formed from two charges ±q separated by a distance b. For large distances r b from the dipole, the electric potential falls like A. 1/r B. 1/ r C. 1/r 3/2 D. 1/r 2 E. 1/r 3 2. Two positive charges are fixed on the x-axis, with q located at x = 0 and 2q located at x = a. At which of the following points is the electric field equal to zero? A. x = a/3 B. x = ( 2 1)a C. x = a/2 D. x = 2a/3 E. x = a/ 2 3. The electric potential in two dimensions is given by Φ(x, y) = xy 2. The electric field vector E(x, y) is therefore given by A. xˆx + y 2 ŷ B. y 2ˆx + xŷ C. y 2ˆx + 2yŷ D. y 2ˆx + 2xyŷ E. (x 2 y 2 /2)ˆx + (xy 3 /3)ŷ

2 PHYS4210 Electromagnetic Theory Quiz 8 Feb Three point charges lie along a line. The two outermost have charge q. The third is midway between then other two, and has charge 2q. This arrangement has A. zero total charge, zero dipole moment, and zero quadrupole moment. B. zero total charge, zero dipole moment, and nonzero quadrupole moment. C. zero total charge, nonzero dipole moment, and zero quadrupole moment. D. zero total charge, nonzero dipole moment, and nonzero quadrupole moment. E. nonzero total charge, nonzero dipole moment, and nonzero quadrupole moment. 2. Consider the following function of position x, for some constant vector a: F (x) = 1 x a Which of the following is the value of the surface integral ˆn F ds for any (closed) surface S which encloses the point x = a? A. 0 B. 1 C. a D. 4π E. 4πa S 3. An infinite conducting sheet lies in the xy plane. A point charge q lies on the z-axis, a distance a above the plane. The charge is attracted to the sheet with a force A. 0 B. q 2 /a 2 C. q 2 /2a 2 D. q 2 /4a 2 E. q 2 /16a 2

3 PHYS4210 Electromagnetic Theory Quiz 22 Feb Two point charges q are separated by a distance a and are otherwise in vacuum. The total energy stored in the electric field set up by the charges is A. q 2 /a if you include the self energy of the charges B. q 2 /a if you neglect the self energy of the charges C. q 2 /a if you include the self energy of the charges D. q 2 /a if you neglect the self energy of the charges E. infinite if you neglect the self energy of the charges 2. A spherically symmetric charge distribution has a charge density ρ(r) = Ar α (in esu/cm 3 ) where A and α are positive constants, and r is the distance from the center. The total charge enclosed by a sphere at radius r is proportional to A. r α B. r 1+α C. r 2+α D. r 3+α E. r 4+α 3. A spherically symmetric charge distribution has a charge density ρ(r) = Ar α (in esu/cm 3 ) where A and α are positive constants, and r is the distance from the center. The electric field at radius r is proportional to A. r α B. r 1+α C. r 2+α D. r 3+α E. r 4+α

4 PHYS4210 Electromagnetic Theory Quiz 1 March Consider two events in spacetime. They are separated by 5 feet to observer A, and they happen 3 nsec apart. To observer B they happen simultaneously. By how much does B see them separated in space? (The speed of light is very close to 1 foot/nsec.) A. 2 feet B. 3 feet C. 4 feet D. 5 feet E. They happen at the same place. 2. Suppose A µ and B ν are two four vectors, and η µν is the standard Minkowski metric tensor. Which of the following is a scalar? A. A ν B. B µ C. A µ B ν D. η µν A µ E. A µ η µν B ν 3. Suppose A µ and B ν are two four vectors, and η µν is the standard Minkowski metric tensor. Which of the following is a (second rank) tensor? A. A ν B. B µ C. A µ B ν D. η µν A µ E. A µ η µν B ν

5 PHYS4210 Electromagnetic Theory Quiz 15 March Given a coordinate transformation matrix a ij and a tensor T, which of the following is the correct expression for T ij, the tensor elements expressed in the transformed coordinate system? A. T ij = k a ij T kk B. T ij = k a ij T kl C. T ij = kl a kl T ij D. T ij = kl a ik a jl T kl E. T ij = kl a ik T kl a lj 2. If A µ = (A 0, A) and B µ = (B 0, B) are contravariant four-vectors in special relativity, which of the following is a correct way of writing their inner product? A. A 0 B 0 + A 1 B 1 + A 2 B 2 + A 3 B 3 B. A 0 B 0 A 1 B 1 A 2 B 2 A 3 B 3 C. A 0 B 0 A B D. All of the above E. None of the above 3. If a µ ν is the Lorentz transformation matrix for a contravariant four-vector, then a µ α a α ν equals which of the following? (The Einstein summation convention is in effect.) A. δ ν µ B. δµ ν C. δα α D. a µ ν E. a α α

6 PHYS4210 Electromagnetic Theory Quiz 22 March An electric dipole consisting of two charges +Q and Q separated by a distance d is placed along the z axis with its center at the origin, as shown below: What is the total electric flux through the xy-plane? A. 0 B. Q C. 4πQ D. Q/d 2 E. 4πQ/d 2 2. What is the magnetic dipole moment for a square loop of wire of side L and carrying a current I? A. IL 2 /c B. πil 2 /c C. IL 2 /4c D. 4πIL 2 /c E. πil 2 /4c 3. A charge q moves with constant velocity v through a region of electric field E and magnetic field B. The vectors v, E, and B are all mutually perpendicular. What is the ratio E/B? A. v B. c C. v/c D. qv/c E. (v/c) 2

7 PHYS4210 Electromagnetic Theory Quiz 29 March Which of the following is not one of Maxwell s Equations? A. E = 4πρ B. B = 0 C. E = (1/c) B/ t D. B = (4π/c)j + (1/c) E/ t E. F = qe + q(v/c) B 2. An esu/cm 2 is the same as which of the following? A. dyne B. gauss C. statvolt D. gauss cm 3 E. erg/gauss 3. A stationary, planar loop of area A sits with its plane perpendicular to a uniform, but time dependent, magnetic field B(t) = kt, where k is a positive constant. The magnitude of the EMF induced in the loop, in CGS units, is A. ka B. kat C. ka/c D. kat/c E. kat/c 2

8 PHYS4210 Electromagnetic Theory Quiz 5 April The force between two charges is proportional to their product and inversely proportional to the square of the distance between them. This empirical fact is called A. Gauss Law B. Ampere s Law C. Faraday s Law D. Coulomb s Law E. Biot-Savart s Law 2. Which of the following is a consequence of applying the principle of special relativity to electrostatics? A. Magnetism B. Stokes theorem C. General relativity D. Quantum mechanics E. The divergence theorem 3. A bar magnet is dropped through a horizontal loop of wire which passes through an ammeter. Some current is detected just as the bar passes inside the loop. This is a demonstration of A. Gauss Law B. Ampere s Law C. Faraday s Law D. Coulomb s Law E. Biot-Savart s Law

9 PHYS4210 Electromagnetic Theory Quiz 12 April Given a four-vector potential A µ = (0, Kct, 0, 0) where K is a constant ant t is time, what are the electric and magnetic fields? A. E = B = 0 B. E = B = Kˆx C. E = 0 and B = Kˆx D. E = Kˆx and B = 0 E. E = Kˆx and B = Kŷ 2. Which of the following describes an electromagnetic wave with x polarization and traveling in the +z direction? (Assume k > 0.) A. E 0ˆx exp( i(ωt kz)) B. E 0ˆx exp( i(ωt + kz)) C. E 0 ẑ exp( i(ωt kx)) D. E 0 ẑ exp( i(ωt + kx)) E. E 0 ŷ exp( i(ωt kz)) 3. The (phase) velocity of an electromagnetic wave moving through a medium with dielectric constant ε and magnetic permittivity µ is A. c B. cεµ C. c/εµ D. c εµ E. c/ εµ

10 PHYS4210 Electromagnetic Theory Quiz 19 April Two identical charges q are placed 2 cm apart. The force between them is 2 dynes. The value of q is A. 1 esu. B. 2 esu. C. 2 esu. D. 2 2 esu. E. 4 esu. 2. A charge of 1 esu moves perpendicularly through a magnetic field of 10, 000 gauss and feels a force of 1 dyne. Its speed is what fraction of the speed of light? A. 1/10000 B. 1/1000 C. 1/100 D. 1/10 E Conductivity σ is defined by the relation j = σe where j is the current density, i.e. current per unit area, and E is the electric field. In the CGS system, the units of conductivity are the same as A. seconds. B. 1/seconds. C. cm. D. 1/cm. E. 1/ohms.

11 PHYS4210 Electromagnetic Theory Quiz 26 April Which of the following is not true about the radiation fields from a moving charge? A. The radiation is in the direction E B. B. E and B are perpendicular to each other. C. Radiation occurs even for nonrelativistic velocities. D. They only arise from charges with nonzero acceleration. E. They are inversely proportional to the square of the source distance. 2. An electromagnetic wave propagates in the z-direction with E(t, x) = E 0 e i(ωt kz). For a circularly polarized wave, E 0 would be proportional to A. ˆx B. ŷ C. ẑ D. ˆx + ŷ E. ˆx + iŷ 3. A charge moves through a dielectric medium with speed v. If n is the index of refraction of the medium, which of the following is the necessary condition if the charge is to emit Čerenkov radiation? A. v < c B. v < nc C. v < c/n D. v > c/n E. v > c/n 2

12 PHYS4210 Electromagnetic Theory Quiz 3 May A long, thin, cylindrical rod of length d and radius R, with d R, sits in an external, uniform magnetic field B whose direction is aligned with the axis of the rod. If the rod is made of a homogenous material with magnetic permittivity µ, what is the magnitude of the magnetic field inside the rod? A. B B. µb C. B/µ D. (R/d)µB E. (R/d)B/µ 2. A single charged particle undergoes simple harmonic motion with angular frequency ω. The average radiated power is proportional to A. ω 0 B. ω 1 C. ω 2 D. ω 3 E. ω 4 3. Two identical charges q are separated by a distance b. The electric dipole moment of this configuration is A. 0 B. qb C. 2qb D. qb/2 E. (qb) 2

13 PHYS4210 Electromagnetic Theory Quiz 10 May A cubical box with perfectly conducting walls supports TM 111 electromagnetic waves in a vacuum. If the sides have length a, what is the frequency of the electromagnetic waves? A. c/3a B. c/a 3 C. c/a D. c 3/a E. 3c/a 2. Two charges sit on the x-axis. One charge has value +q and sits at x = a. The other charge has value 4q and sits at x = +2a. The electric field at the origin is A. 0 B. q/a 2 C. 2q/a 2 D. q/a 2 E. 2q/a 2 3. Two long parallel wires each carry the same amount of current. If the separation distance and current are both doubled, the force between the wires is A. unchanged. B. divided by 2. C. divided by 4. D. multiplied by 2. E. multiplied by 4.