# What is the meaning of integral of negative magnetic field (nT) over time?

I have a plot of the magnetic field (y-axis) over time (x-axis), one measure each hour (Dst - Disturbance Storm-Time).

From time to time, there is a negative peak, which indicates a magnetic storm. The more it goes down the bigger the storm.

What is the physical meaning of the integral of it (nT x h)?

• Can you show your plot? Dec 25 '16 at 18:57
• It's there my friend. Dec 25 '16 at 20:01
• To be clear, are you saying your y-axis is in nano-teslas, and your x axis is in days, while the points on the plot indicate one hour each? What is the source of this information? How is the magnetic field measured? Dec 26 '16 at 2:28
• That is the Dst index for 2015. Don't know from where the data I have came from but it's pretty similar to wdc.kugi.kyoto-u.ac.jp/dst_realtime/201501/index.html. Does it helps to answer the question? Dec 26 '16 at 10:22
• It depends how you want to use the integral. You can easily find the average value of the magnetic field in nT between say 1 hr and 2hrs recording time using integration.
– Jay
Mar 10 '17 at 1:20

Disturbance storm time index is a measure of the weakened horizontal component of Earth magnetic field during great magnetic disturbances. The depression is often flanked by peaks, that initiates and ends the storm. Dst is published by Kyoto University and more information about the methods and references are available on the web page.

The Dst index represents the axially symmetric disturbance magnetic field at the dipole equator on the Earth's surface. Major disturbances in Dst are negative, namely decreases in the geomagnetic field. These field decreases are produced mainly by the equatorial current system in the magnetosphere, usually referred to as the ring current. The neutral sheet current flowing across the magnetospheric tail makes a small contribution to the field decreases near the Earth. Positive variations in Dst are mostly caused by the compression of the magnetosphere from solar wind pressure increases.

Sugiura and Kamei, IAGA Bulletin No 40 (1991)

Measures are presented as the deviation from the average magnetic field strength, measured in the SI unit Tesla $T$ at time $t$. In this context, the magnetic field is very weak, so the nano prefix $n$ is usually used. Magnetic field strength can be derived from weight (in $kg$), electric charge (in Coulomb $C$) and time in second ($s$) as:

$T =\frac{kg}{C \times s}$

if you integrate with time (in seconds, $s$) you'll get for each unit:

$T \times s =\frac{kg}{C}$.

The relation of electric charge and weight is used as a measure of Radiation exposure, often given in röntgen ($R$) and related as:

$1 \frac{C}{kg} = 3876 R$

Technically, your integral will, therefore, be a measure of increased radiation exposure, kinetic energy released per unit mass, for the time you integrate over. You could convert it to röntgen ($2.58×10^{−4} C/kg = R$) but note that the calculated product describes the deviation, not the absolute ionization.