B-field Component of Electromagnetic Wave After Change in Time

In summary, the y component of the magnetic field at point O at time 0.227*E-16 s can be found using the formula B = B_0*sin(pi/2 - 2Pi*f*t), where B_0 is the given maximum value for the magnetic field, f is the given frequency, and t is the given time. The maximum value for the sin portion of the function is 1, which occurs when kx = pi/2. The function works with either a + or - in front of the (wt) term, and the resultant formula is B = B_0*sin(pi/2 - 2Pi*f*t).
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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,
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  • #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?
 
  • #3
katastrophe said:
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)

Reply back if this helps!

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What is the B-field component of an electromagnetic wave?

The B-field component of an electromagnetic wave refers to the magnetic field that is created as a result of the changing electric field. It is one of the two components that make up an electromagnetic wave, the other being the electric field.

How does the B-field component change after a change in time?

After a change in time, the B-field component of an electromagnetic wave also changes. This change is due to the relationship between the electric and magnetic fields in an electromagnetic wave, known as Maxwell's equations.

What factors can affect the B-field component of an electromagnetic wave?

The B-field component of an electromagnetic wave can be affected by various factors, such as the strength and direction of the electric field, the speed of the wave, and the medium through which the wave is traveling.

Why is the B-field component important in understanding electromagnetic waves?

The B-field component plays a crucial role in understanding electromagnetic waves because it is responsible for the creation of a magnetic field, which is essential for the wave's propagation and interaction with other objects. Additionally, the B-field component is closely related to the electric field component, making it a vital aspect of electromagnetic wave behavior.

How is the B-field component measured and represented?

The B-field component of an electromagnetic wave can be measured using a device called a magnetometer. It is typically represented by a vector quantity, with its direction and magnitude indicating the strength and orientation of the magnetic field at a given point in space.

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