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PHYS1250 Fundamental Physics

Assignment Four

Due Date: November 30, 2023

The magnitude of gravitational acceleration is denoted by g throughout this paper.

The problems in this paper have a wide range of difficulties. They are specially designed to strengthen students’ concepts and to develop the problem solving skills. Students are expected to drill the prob-lems with perseverance.

1. A rectangular coil consists of N = 100 closely wrapped turns and has dimensions a = 0.400 m and b = 0.300 m The coil is hinged along the y axis, and its plane makes an angle θ = 30.0o with the x axis.

(a) What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = 0.800 T directed in the positive x direction when the current is I = 1.20 A in the direction shown? (7 marks)

(b) What is the expected direction of rotation of the coil? (3 marks)

2. Find (a) the equivalent capacitance of the capacitors in the figure, (b) the charge on each capacitor, and (c) the potential difference across each capacitor. (18 marks)

3. Four charges each having charge Q are located at the corners of a square having sides of length a. Find expressions for the following problems.

(a) The total electric field at the center of the square due to the four charges. (6 marks)

(b) The total electric potential at the center of the square due to the four charges. (6 marks)

(c) The work required by an external agent to bring a fifth charge q from infinity to the center of the square. (6 marks)

4. A square wire loop with 2.00m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field. The loop contains a 20.0V battery with negligible internal resistance. The magnitude of the field varies with time according to the formula, B = 0.04 − 0.90t, with B in teslas and t in seconds. The following figure shows the square wire loop and the B-field at t = 0.

(a) What is the net emf in the circuit? (6 marks)

(b) Determine the direction of the current through the battery. Discuss the use of Lenzs law in your determination. (4 marks)

5. Light of wavelength 620 nm falls on a double slit, and the first bright fringe of the interference pattern is seen at an angle of 15.0 o with the horizontal. Find the separation between the slits. (10 marks)

6. A material having an index of refraction of 1.30 is used as an antireflective coating on a piece of glass (n = 1.50). What should the minimum thickness of this film be to minimize reflection of 500-nm light? (10 marks)

7. Two glass plates 10.0 cm long are in contact at one end and separated at the other end by a thread with a diameter d = 0.0500 mm. Light containing the two wavelengths 400 nm and 600 nm is incident perpendicularly and viewed by reflection. At what distance from the contact point is the next dark fringe? (12 marks)

8. A diffraction grating with 355 lines/mm is 1.00 m in front of a screen. What is the wavelength of light whose first-order maxima will be 16.4 cm from the central maximum on the screen? (12 marks)