Find B-Field from E-Field: Correct Answer Revealed

In summary, the conversation is about finding H in free space using the equation (\nabla X E ) = -dB/dt and integrating it with respect to t. The correct answer is H = 0.4 w*(eps) *cos(\omegat-50x) \widehat{z}, and it is important to remember that H and B are not the same. The equations D = eps*E and H = B/mu are also mentioned, as well as the fact that the curl pertains to spatial derivatives, not temporal.
  • #1
radiator
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0

Homework Statement



E = 20 cos([tex]\omega[/tex]t-50x) [tex]\widehat{y}[/tex] find H in free space?

Homework Equations



I used ([tex]\nabla[/tex] X E ) = -dB/dt , and then integrated that expression with respect to t , for some reason I am getting an incorrect answer ?!

The Attempt at a Solution



the correct answer is H = 0.4 w*(eps) *cos([tex]\omega[/tex]t-50x) [tex]\widehat{z}[/tex]
 
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  • #2
radiator said:
I used ([tex]\nabla[/tex] X E ) = -dB/dt , and then integrated that expression with respect to t , for some reason I am getting an incorrect answer ?!

The Attempt at a Solution



the correct answer is H = 0.4 w*(eps) *cos([tex]\omega[/tex]t-50x) [tex]\widehat{z}[/tex]
remember that H and B are not the same.

D = eps*E
and
H = B/mu

also:

( [tex]\nabla[/tex] X H ) = -dD/dt

or for linear media:( [tex]\nabla[/tex] X B ) = mu*eps*dE/dt
also remember that the curl pertains to spatial, not temporal derivatives.
 

1. What is the relationship between B-Field and E-Field?

The B-Field and E-Field are both components of the electromagnetic field. The E-Field, also known as the electric field, is produced by electric charges and exerts a force on other electric charges. The B-Field, also known as the magnetic field, is produced by moving electric charges and exerts a force on other moving electric charges.

2. How do you calculate the B-Field from a given E-Field?

The B-Field can be calculated from the E-Field using the formula B = (u/ε) * E, where u is the permeability of the medium and ε is the permittivity of the medium. The units for B-Field are Tesla (T) or Gauss (G) and the units for E-Field are Volts per meter (V/m).

3. Can the B-Field and E-Field exist independently of each other?

No, the B-Field and E-Field are always present together and are interconnected. Changes in one field can cause changes in the other field.

4. What is the significance of finding the B-Field from the E-Field?

Finding the B-Field from the E-Field helps us understand and predict the behavior of electromagnetic waves, which are essential for many technologies such as communication systems, medical imaging, and energy production.

5. Are there any real-life applications of finding the B-Field from the E-Field?

Yes, there are many real-life applications of finding the B-Field from the E-Field. Some examples include MRI machines, particle accelerators, and electric motors. Understanding the relationship between these fields also helps in the development of new technologies and advancements in existing ones.

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