Chapter 22. Average energy density in an electromagnetic wave (22-24)

Question

delWIiL1WYDXKYqYxazM4k8LOJJpj2iCAY3g2CCsg9R5ARcq8aBWe4kQVeSMm8KyUzG9eEpovOA=
{"title":"Average energy density in an electromagnetic wave","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,24,9,38\"}]"} {"title":"Electric field magnitude","description":"Incorrect","type":"incorrect","color":"#008000","code":"[{\"shape\":\"rect\",\"coords\":\"98,21,113,35\"}]"} {"title":"Electric field rms value","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"150,19,167,37\"}]"} {"title":"Magnetic field magnitude","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"215,7,231,24\"}]"} {"title":"Magnetic field rms value","description":"Incorrect","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"262,7,277,24\"}]"} {"title":"Permeability of free space","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"274,35,286,48\"},{\"shape\":\"rect\",\"coords\":\"222,37,238,53\"}]"} {"title":"Permittivity of free space","description":"Incorrect","type":"incorrect","color":"#ff99cc","code":"[{\"shape\":\"rect\",\"coords\":\"138,21,149,36\"},{\"shape\":\"rect\",\"coords\":\"83,22,96,39\"}]"}

Question

Q4oipdn96VapCbbhTzlAaM4nrMshCjs8N4LNQQ==
{"title":"Average energy density in an electromagnetic wave","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,24,9,38\"}]"} {"title":"Electric field magnitude","description":"Correct!","type":"correct","color":"#008000","code":"[{\"shape\":\"rect\",\"coords\":\"98,21,113,35\"}]"} {"title":"Electric field rms value","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"150,19,167,37\"}]"} {"title":"Magnetic field magnitude","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"215,7,231,24\"}]"} {"title":"Magnetic field rms value","description":"Incorrect","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"262,7,277,24\"}]"} {"title":"Permeability of free space","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"274,35,286,48\"},{\"shape\":\"rect\",\"coords\":\"222,37,238,53\"}]"} {"title":"Permittivity of free space","description":"Incorrect","type":"incorrect","color":"#ff99cc","code":"[{\"shape\":\"rect\",\"coords\":\"138,21,149,36\"},{\"shape\":\"rect\",\"coords\":\"83,22,96,39\"}]"}

Question

Ko+Bwd4cCS/72p2OLfE4zFk7NyTlqxu41y4kDw==
{"title":"Average energy density in an electromagnetic wave","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,24,9,38\"}]"} {"title":"Electric field magnitude","description":"Wrong","type":"incorrect","color":"#008000","code":"[{\"shape\":\"rect\",\"coords\":\"98,21,113,35\"}]"} {"title":"Electric field rms value","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"150,19,167,37\"}]"} {"title":"Magnetic field magnitude","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"215,7,231,24\"}]"} {"title":"Magnetic field rms value","description":"Incorrect","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"262,7,277,24\"}]"} {"title":"Permeability of free space","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"274,35,286,48\"},{\"shape\":\"rect\",\"coords\":\"222,37,238,53\"}]"} {"title":"Permittivity of free space","description":"Incorrect","type":"incorrect","color":"#ff99cc","code":"[{\"shape\":\"rect\",\"coords\":\"138,21,149,36\"},{\"shape\":\"rect\",\"coords\":\"83,22,96,39\"}]"}

Question

ZQ/e8+VSfx6ZtpIHF0qSN6PrUR4iNzPTbWTJsw==
{"title":"Average energy density in an electromagnetic wave","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,24,9,38\"}]"} {"title":"Electric field magnitude","description":"Wrong","type":"incorrect","color":"#008000","code":"[{\"shape\":\"rect\",\"coords\":\"98,21,113,35\"}]"} {"title":"Electric field rms value","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"150,19,167,37\"}]"} {"title":"Magnetic field magnitude","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"215,7,231,24\"}]"} {"title":"Magnetic field rms value","description":"Incorrect","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"262,7,277,24\"}]"} {"title":"Permeability of free space","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"274,35,286,48\"},{\"shape\":\"rect\",\"coords\":\"222,37,238,53\"}]"} {"title":"Permittivity of free space","description":"Incorrect","type":"incorrect","color":"#ff99cc","code":"[{\"shape\":\"rect\",\"coords\":\"138,21,149,36\"},{\"shape\":\"rect\",\"coords\":\"83,22,96,39\"}]"}

Question

i7h9vvBqI98fS/1vo+YIVk412daDh4KghL20Sg==
{"title":"Average energy density in an electromagnetic wave","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,24,9,38\"}]"} {"title":"Electric field magnitude","description":"Wrong","type":"incorrect","color":"#008000","code":"[{\"shape\":\"rect\",\"coords\":\"98,21,113,35\"}]"} {"title":"Electric field rms value","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"150,19,167,37\"}]"} {"title":"Magnetic field magnitude","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"215,7,231,24\"}]"} {"title":"Magnetic field rms value","description":"Correct!","type":"correct","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"262,7,277,24\"}]"} {"title":"Permeability of free space","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"274,35,286,48\"},{\"shape\":\"rect\",\"coords\":\"222,37,238,53\"}]"} {"title":"Permittivity of free space","description":"Incorrect","type":"incorrect","color":"#ff99cc","code":"[{\"shape\":\"rect\",\"coords\":\"138,21,149,36\"},{\"shape\":\"rect\",\"coords\":\"83,22,96,39\"}]"}

Question

c5rMJ+SPmL5HoFBkbIrvNybqiLx+QiOn0hdOAWs9CMs=
{"title":"Average energy density in an electromagnetic wave","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,24,9,38\"}]"} {"title":"Electric field magnitude","description":"Wrong","type":"incorrect","color":"#008000","code":"[{\"shape\":\"rect\",\"coords\":\"98,21,113,35\"}]"} {"title":"Electric field rms value","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"150,19,167,37\"}]"} {"title":"Magnetic field magnitude","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"215,7,231,24\"}]"} {"title":"Magnetic field rms value","description":"Wrong","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"262,7,277,24\"}]"} {"title":"Permeability of free space","description":"Correct!","type":"correct","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"274,35,286,48\"},{\"shape\":\"rect\",\"coords\":\"222,37,238,53\"}]"} {"title":"Permittivity of free space","description":"Incorrect","type":"incorrect","color":"#ff99cc","code":"[{\"shape\":\"rect\",\"coords\":\"138,21,149,36\"},{\"shape\":\"rect\",\"coords\":\"83,22,96,39\"}]"}

Question

vBkI+Vt8MfnYrBL3sYTzTrVSmjHBcILzDs8PMOotkU0=
{"title":"Average energy density in an electromagnetic wave","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,24,9,38\"}]"} {"title":"Electric field magnitude","description":"Wrong","type":"incorrect","color":"#008000","code":"[{\"shape\":\"rect\",\"coords\":\"98,21,113,35\"}]"} {"title":"Electric field rms value","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"150,19,167,37\"}]"} {"title":"Magnetic field magnitude","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"215,7,231,24\"}]"} {"title":"Magnetic field rms value","description":"Wrong","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"262,7,277,24\"}]"} {"title":"Permeability of free space","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"274,35,286,48\"},{\"shape\":\"rect\",\"coords\":\"222,37,238,53\"}]"} {"title":"Permittivity of free space","description":"Correct!","type":"correct","color":"#ff99cc","code":"[{\"shape\":\"rect\",\"coords\":\"138,21,149,36\"},{\"shape\":\"rect\",\"coords\":\"83,22,96,39\"}]"}

Review

The value of \(u\) at any position varies with time, so it’s often more useful to state its average value. The average value of the cosine function squared is \(1/2\), so

In Equation 22-24 we’ve used the root-mean-square (rms) values of the oscillating electric and magnetic fields, \(E_{\mathrm{average}} = E_0\ / \sqrt{2}\) and \(B_{\mathrm{rms}} = B_0\ / \sqrt{2}\) (see Section 21-2).