Physics 114 Exam III

Answer each of the following 4 questions and each of the following 4 problems. Each question is worth 10 points each and each problem is worth 15 points. Be sure to show all your work.

Questions

1. Find the direction of the current (if there is one) in the resistor shown below (that is does it go to the left or to the right) (a) at the instant after the switch is closed, (b) after the switch has been closed for a long time and (c) at the instant after the switch is reopened.

2. A planar electromagnetic wave is propagating through space. Its electric field vector is given by E = E_o cos(ky – wt) , where k is 5 x 10⁷ 1/m, and E_o is 100 N/C. (a) What is w?(b) What is the magnetic field vector (magnitude and direction)? (c) Write down the poynting vector. (magnitude and direction).

3. (a) Does light traveling from one medium to another always bend toward the normal? (b) As light travels across the interface between two media, does its frequency change? (c) Its wavelength? (d) Its velocity? Explain your answers.

4. A thin converging lens is used to form a real image of a nearby object. If the object is moved closer to the lens, a new real image is observed. Does the new image differ from the old one (a) in position relative to the lens, and (b) in size? If it does, describe how.

Problems

1. Two parallel loops of wire having a common axis are shown below. The smaller loop (radius r = 0.1 m) is above the larger loop by a large distance x>>R, with R = 0.5 m. Consequently the magnetic field due to the current, I = i = 2A, in the larger loop is (to a good approximation) constant throughout the smaller loop. The value of this field (obtainable from the law of Biot and Savart) is given by B(x) = m₀m/(2px³), where m is the magnetic moment (= NIA). Suppose that x is increasing at a constant rate dx/dt = v = 3 m/s. When x = 10 m find (a) The flux through the smaller loop (b) the induced emf in the smaller loop and (c) the direction the induced current. For part c specify whether the induced current is in the same or opposite direction as i. Note that dB/dt = -(3vm₀m)/(2px⁴) through the top loop.

2. Three polarizing disks, the planes of which are parallel, are all centered on a common axis. The direction of the transmission axis is shown below relative to the common vertical direction. A plane, unpolarized beam of light is incident from the left on the first disk with an intensity = 10 W/m². Calculate the intensity (a) after the first disk if q₁ is 10^o, (b) after the second disk if q₂ is 40^o, (c) after the third disk if q₃ is 10^o, and (d) after the third disk if q₁ is still 10^o and q₂ is still 40^o but the third disk is now rotated so that q₃ = 40^o.

3. When the light in the figure shown below passes through the glass block, it is shifted laterally by the distance d. The index of refraction of the glass is 1.5 (a) Find the angle of refraction when the beam passes from air into the glass. (b) Find the angle of refraction when the beam passes from the glass back into the air. (c) Find the value of d.

4. (a) A concave mirror forms an inverted image four times larger than the object. Find the focal length of the mirror if the distance between the object and the image is 0.600 m. (b) A convex mirror forms a virtual image half the size of the object. If the distance between the image and the object is 20.0 cm, determine the radius of curvature of the mirror.