PHYS 2212 Module 12 Self Assessment Practice Problems

Module 12 Self Assessment Practice Problems

12.1
In a region of space, the electric field is pointed along the x-axis, but its magnitude changes as described by E_x = (10 N/C) sin(20x – 500t) and E_y = E_z = 0 where t is in nanoseconds and x is in cm. Find the displacement current through a circle of radius 3 cm in the x = 0 plane at t = 0.
Answer: 0.125 A

12.3
Radio station WCCO in Minneapolis broadcasts at a frequency of 830 kHz. At a point some distance from the transmitter, the magnetic-field amplitude of the electromagnetic wave from WCCO is 4.82 x 10^-11 T.
(a) Find the wavelength.
(b) Find the wave number.
(c) Calculate the angular frequency.
(d) Calculate the electric-field amplitude.
Answer: (a) 361 m (b) 0.017 m^-1(c) 5.22 x 10⁶ rad/s (d) 0.014 V/m

12.4
The electric field of a sinusoidal electromagnetic wave obeys the equation E=(375 V/m) cos[(1.99 x 10⁷ rad/m)x + (5.97 x 10¹⁵ rad/s)t]
(a) What is the speed of the wave?
(b) What is the amplitude of the electric field of this wave?
(c) What is the amplitude of the magnetic field of this wave?
(d) What is the frequency of the wave?
(e) What is the wavelength of the wave?
(f) What is the period of the wave?
Answer: (a) 3 x 10⁸ m/s = c (b) 375 V/m (c) 1.25 µT (d) 950 THz (e) 316 nm (f) 1.05 fs

12.5
A certain microwave oven projects 1.00 kW of microwaves onto a 30-cm-by-40-cm area.
(a) What is its intensity in W/m²?
(b) Calculate the maximum electric field strength E₀ in these waves.
(c) What is the maximum magnetic field strength B₀?
Answer: (a) 8.3 kW/m²(b) 2.5 kV/m (c) 8.3 µT

12.6
Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of 10¹² W) pulses of light that last for an extremely short time (a few nanoseconds). These short pulses scramble the interior of a cell without causing it to explode, as long pulses would do. We can model a typical such cell as a disk 5.0 µm in diameter, with the pulse lasting for 4.0 ns with an average power of 2.0 x 10¹² W. We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse.
(a) How much energy is given to the cell during this pulse?
(b) What is the intensity (in W/m²) delivered to the cell?
(c) What are the maximum values of the electric and magnetic fields in the pulse?
Answer: (a) 80 J/cell (b) 1.02 x 10²¹ W/m²(c) 8.8 x 10¹¹ V/m, 2921 T

12.7
A satellite 575 km above the earth’s surface transmits sinusoidal electromagnetic waves of frequency 92.4 MHz uniformly in all directions, with a power of 25.0 kW.
(a) What is the intensity of these waves as they reach a receiver at the surface of the earth directly below the satellite?
(b) What are the amplitudes of the electric and magnetic fields at the receiver?
(c) If the receiver has a totally absorbing panel measuring 15.0 cm by 40.0 cm oriented with its plane perpendicular to the direction the waves travel, what average force do these waves exert on the panel? Is this force large enough to cause significant effects?
Answer: (a) 6 nW/m²(b) 2.1 mV/m, 7.1 pT (c) 1.2 x 10^-18 N

12.8
The energy flow to the earth from sunlight is about 1.4 kW/m².
(a) Find the maximum values of the electric and magnetic fields for a sinusoidal wave of this intensity.
(b) The distance from the earth to the sun is about 1.5 x 10¹¹ m. Find the total power radiated by the sun.
Answer: (a) 1.03 kV/m, 3.4 µT (b) 3.96 x 10²⁶ W

12.10
A microscopic spherical dust particle of radius 2 µm and mass 10 µg is moving in outer space at a constant speed of 30 cm/sec. A wave of light strikes it from the opposite direction of its motion and gets absorbed. Assuming the particle decelerates uniformly to zero speed in one second, what is the average electric field amplitude in the light?
Answer: 7.3 x 10⁶ V/m