Question
If electric and magnetic field strengths vary sinusoidally in time, being zero at t=0t=0 , then E=E0sin2πftE = E_0 \sin{2\pi f t} and B=B0sin2πftB = B_0 \sin{2\pi f t} . Let f=1.00 GHzf = 1.00 \textrm{ GHz} here. (a) When are the field strengths first zero? (b) When do they reach their most negative value? (c) How much time is needed for them to complete one cycle?
Question by OpenStax is licensed under CC BY 4.0
Final Answer
  1. t=0 st = 0 \textrm{ s}
  2. 7.5×1010 s7.5\times 10^{-10}\textrm{ s}
  3. 1.00×109 s1.00\times 10^{-9}\textrm{ s}

Solution video

OpenStax College Physics, Chapter 24, Problem 46 (Problems & Exercises)

OpenStax College Physics, Chapter 24, Problem 46 (PE) video thumbnail

In order to watch this solution you need to have a subscription.

Start free trial Log in
vote with a rating of votes with an average rating of .

Calculator Screenshots

  • OpenStax College Physics, Chapter 24, Problem 46 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. The frequency of an electromagnetic wave is 1.00 gigahertz suppose and its electric field strength is equal to the peak electric field strength times sin of 2π times its frequency times time and then the magnetic field strength is an analogous formula but where we have peak magnetic field strength in place of peak electric field strength. The question in part (a) is asking when will these two fields first be zero? So we have to solve this equation in other words and we can divide both sides by E naught in which case we have sin 2πft equals 0. So when is sin of something zero? That occurs when you have the something... the argument of sin, which is 2π times frequency times time in this case equal to either 0 or π or or and the first zero then is this one here when time is zero. So at the very beginning at 0 seconds is when both the electric field and the magnetic field are zero. Part (b) is asking when they are the most negative? Well, the range of sin is from negative 1 upto 1 and so the smallest value that's possible for this sin is negative 1 and so we can solve this equation then sin of 2πft equals negative 1 and that occurs when the argument for sin is 3π over 2 or you know that plus π or 7π over 2 as well but anyway, we want the first time that it's most negative or the first solution to this equation. And so then we can divide both sides by 2π times frequency and we have 3π over 2π times 2 times frequency and the π's cancel and then we have 2 times 2 is 4 on the bottom so that's 3 over 4 times the frequency of 1.00 times 10 to the 9 hertz and that is 7.5 times 10 to the minus 10 seconds is the first time at which point you have the most negative electric and magnetic fields. Part (c) is asking for the time it takes to do one complete cycle which is another way of asking what is the period of this periodic wave? And that is the reciprocal of its frequency which is 1 over 1.00 times 10 to the 9 hertz and so that is 1.00 times 10 to the minus 9 seconds.