Transient Magnetic Fields pp 111-126 | Cite as

# Radiated Energy for General Current Ramps

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## Abstract

As discussed in Chap. 4, the Poynting flux and field energy are balanced by a source term, −**J**⋅**E**, as given in Eq. ( 4.5). Thus, we can obtain the radiated energy by subtracting the field energy, \((3/2)\mathcal {E}_{0}\), from the total energy obtained by integrating the source term over the duration of the transient. This is computationally easier than performing a surface integral of the Poynting flux, which involves the product of the two factors, *∂F*∕*∂r* and *∂F*∕*∂r*_{L}. On the other hand, the surface integral leads to a physically interesting way of interpreting the radiation in terms of the bends in the profile of the current ramp. Consequently, we shall describe these two approaches separately in our consideration of generalized current ramps in the next two subsections.

## References

- Leighton RB (1959) Principles of modern physics. McGraw-Hill, New York, p 409Google Scholar