16.5 The electromagnetic spectrum  (Page 9/19)

During normal beating, the heart creates a maximum 4.00-mV potential across 0.300 m of a person’s chest, creating a 1.00-Hz electromagnetic wave. (a) What is the maximum electric field strength created? (b) What is the corresponding maximum magnetic field strength in the electromagnetic wave? (c) What is the wavelength of the electromagnetic wave?

Distances in space are often quoted in units of light-years, the distance light travels in 1 year. (a) How many meters is a light-year? (b) How many meters is it to Andromeda, the nearest large galaxy, given that it is $2.54\times {10}^6$ ly away? (c) The most distant galaxy yet discovered is $13.4\times {10}^9$ ly away. How far is this in meters?

A certain 60.0-Hz ac power line radiates an electromagnetic wave having a maximum electric field strength of 13.0 kV/m. (a) What is the wavelength of this very-low-frequency electromagnetic wave? (b) What type of electromagnetic radiation is this wave (b) What is its maximum magnetic field strength?

(a) What is the frequency of the 193-nm ultraviolet radiation used in laser eye surgery? (b) Assuming the accuracy with which this electromagnetic radiation can ablate (reshape) the cornea is directly proportional to wavelength, how much more accurate can this UV radiation be than the shortest visible wavelength of light?

In a region of space, the electric field is pointed along the x -axis, but its magnitude changes as described by
$\begin{array}{c}{E}_x=\left(10\text{N/C}\right)\text{sin}\left(20x-500t\right)\hfill \\ E_y=E_z=0\hfill \end{array}$
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 $t=0$ .

A microwave oven uses electromagnetic waves of frequency $f=2.45\times {10}^9\text{Hz}$ to heat foods. The waves reflect from the inside walls of the oven to produce an interference pattern of standing waves whose antinodes are hot spots that can leave observable pit marks in some foods. The pit marks are measured to be 6.0 cm apart. Use the method employed by Heinrich Hertz to calculate the speed of electromagnetic waves this implies.

Galileo proposed measuring the speed of light by uncovering a lantern and having an assistant a known distance away uncover his lantern when he saw the light from Galileo’s lantern, and timing the delay. How far away must the assistant be for the delay to equal the human reaction time of about 0.25 s?

Show that the wave equation in one dimension
$\frac{{\partial }^{2}f}{\partial x^2}=\frac{1}{v^2}\frac{{\partial }^{2}f}{\partial t^2}$
is satisfied by any doubly differentiable function of either the form $f\left(x-vt\right)$ or $f\left(x+vt\right)$ .

On its highest power setting, a microwave oven increases the temperature of 0.400 kg of spaghetti by $45.0\text{°}\text{C}$ in 120 s. (a) What was the rate of energy absorption by the spaghetti, given that its specific heat is $3.76\times {10}^3\text{J/kg}·\text{°}\text{C}$ ? Assume the spaghetti is perfectly absorbing. (b) Find the average intensity of the microwaves, given that they are absorbed over a circular area 20.0 cm in diameter. (c) What is the peak electric field strength of the microwave? (d) What is its peak magnetic field strength?