# B-field Component of Electromagnetic Wave After Change in Time

## Homework Statement

What is the y component of the magnetic field at point O at time 0.227*E-16 s?
Given: Frequency: 2.20*E16 Hz
Max value of B-field: 4.00*E-8T when t = 0 at point O

## Homework Equations

I think the following two equations could potentially be applied to the problem:
B = B_max*sin(kx-wt)

## The Attempt at a Solution

I know w = 2*Pi*f (where f is the given frequency)
t = the given time
I guess I'm not sure how to find k & x, or if this is even the correct manner in which to solve the problem.

Thanks,
x^2

I have this problem as well, but haven't gotten much further than you. I have set k=2pi/wavelength, with wavelength = c/f. I'm a bit torn on how to get x properly. I was thinking that if you have wavelength, and you could find the fraction of the period it was through at that point, you could multiply that by the wavelength in order to obtain x, but I don't know if that's the right way to do it.

However, doing all of this, I have still obtained the wrong answer. Have you had any further insights?

I have this problem as well, but haven't gotten much further than you. I have set k=2pi/wavelength, with wavelength = c/f. I'm a bit torn on how to get x properly. I was thinking that if you have wavelength, and you could find the fraction of the period it was through at that point, you could multiply that by the wavelength in order to obtain x, but I don't know if that's the right way to do it.

However, doing all of this, I have still obtained the wrong answer. Have you had any further insights?
Yes, I have figured it out.....

B = B_0*sin(kx - wt)
B_0 is the given maximum value for the magnetic field. w = 2pi*f, where f is the given frequency. t is time, and it is given.
You know the maximum value for the sin portion of the function is 1, as this is when you would get B_0 (B_0 * 1 = B_0). What value maximizes the sin function such that it equal 1? pi/2....so you therefore know that kx = pi/2 and (wt) is the shift that takes into account frequency and time. The function works with either a + or a - in front of the (wt) because of the symmetry of the function. If you get a negative value, just be sure to use the absolute value.

I noticed that I happened to get the original max value of my magnetic field. This makes me think that perhaps the point of the problem was to show that in the given time x total periods of the wave were made, but on the other hand it could just be coincidence.

Either way, the resultant formula is:

B = B_0*sin(pi/2 - 2Pi*f*t)