Electricity and Magnetism Quiz

If charge +Q is located in space at the point (x = 1 m, y = 10 m, z = 5 m), what is the total electric flux that passes through the *yz*-plane?

• ∞

• 1

• Q / ε₀

• Q / (2ε₀)

• 0

A point charge Q is placed at the center of a hollow, conducting spherical shell of inner radius a and outer radius b, as shown above. A net charge q is placed on the conducting shell. If the electric potential is assumed to be 0 at infinity, the magnitude of the electric potential at r, where a < r < b, is

• 0

• Q / (4πε₀r)

• (Q + q) / (4πε₀r)

• Q / (4πε₀a)

• (Q + q) / (4πε₀b)

The figure above shows three arrangements of one electron (e) and two protons (p). Which of the following is true about the magnitude F of the net electrostatic force acting on the electron due to the protons?

• F₁ > F₂ > F₃

• F₁ = F₂ > F₃

• F₁ > F₃ > F₂

• F₂ > F₁ > F₃

• F₂ > F₃ > F₁

A series AC circuit with impedance Z consists of resistor R, inductor L, and capacitor C, as shown above. The ideal emf source has a sinusoidal output given by E = Eₐₓ sin(ωt), and the current is given by I = Iₐₓ sin(ωt − φ). What is the average power dissipated in the circuit? (I₍ᵣ₎ is the root-mean-square current.)

• I²ᵣ R

• ½ I²ᵣ R

• ½ I²ᵣ Z

• ½ I²ᵣ R cosφ

• ½ I²ᵣ Z cosφ

The quantum efficiency of a photon detector is 0.1. If 100 photons are sent into the detector, one after the other, the detector will detect photons

• exactly 10 times

• an average of 10 times, with an rms deviation of about 0.1

• an average of 10 times, with an rms deviation of about 1

• an average of 10 times, with an rms deviation of about 2

• an average of 10 times, with an rms deviation of about 3

Two students perform an experiment in which they drop a ball from rest from a known height above the ground and measure the speed of the ball just before it strikes the ground. From repeated measurement, the students estimate the uncertainty in the measured speed of the ball to be 10 percent. Which of the following gives the uncertainty in the kinetic energy of the ball? (Assume the uncertainty in the ball’s mass is negligibly small.)

• 5%

• 10%

• 15%

• 20%

• 40%

Which of the following wave functions represents a solution to the Schrödinger equation for an electron in the 2s state of a hydrogen atom? (c is a constant and a₀ is the Bohr radius.)

• c cosθ

• c exp(−r / a₀)

• c (1 − r / 2a₀) exp(−r / 2a₀)

• c (1 − r / 2a₀) exp(−r / 2a₀) cosθ

• c (1 − r / 2a₀) exp(−r / 2a₀) sinθ exp(±iφ)

A particle in an infinite square well has as its initial wave function an equal mixture of the first three orthonormal stationary states: Ψ(x,0) = A [ψ₁(x) + ψ₂(x) + ψ₃(x)] The value of the normalization constant A is equal to which of the following?

• 1 / √3

• 1 / √2

• 1

• √2

• √3

A matter wave of energy E > 0 and wave number k is incident from the left on a potential well of width L and depth V₀. The top of the well is at zero energy and the bottom of the well is at −V₀, as shown in the figure above. The spatial part of the wave function in region 3 has which of the following forms? (A is a constant.)

• A eᶦᵏˣ

• A sin(kx)

• A cos(kx)

• A eᶦᵏˣ + B e⁻ᶦᵏˣ

• A e⁻ᵏˣ (k real and positive)

1 has force constant k₁ and spring 2 has force constant k₂, where k₁ > k₂. If the same external force is applied to both springs, which of the following is true about the extensions (Δx₁ and Δx₂) and the stored potential energies (U₁ and U₂) of the two springs?

• Δx₁ < Δx₂, U₁ < U₂

• Δx₁ < Δx₂, U₁ > U₂

• Δx₁ = Δx₂, U₁ < U₂

• Δx₁ = Δx₂, U₁ = U₂

• Δx₁ > Δx₂, U₁ = U₂