# To store 1 Coulomb of charge [closed]

One teacher told me that to store 1Coulomb charge we need a material of about 7 times of Earth. And another teacher told me that what he said was wrong. who is correct?

• You can easily store 1 Ampere hour = 3600 Coulomb in a small battery. – Thomas Fritsch Sep 4 '19 at 16:11
• @Thomas that's not a correct interpretation of that energy content - that amount of charge is never isolated. – Emilio Pisanty Sep 4 '19 at 17:52
• 1 F capacitor – Farcher Sep 4 '19 at 21:42

What you need to store 1 C of charge depends on what you mean by storage and under what conditions this charge will be stored, but with realistic restrictions it is highly unlikely that you would need anywhere near the mass of the Earth. If storing the charge in a capacitor or battery is acceptable, then as other answers have pointed out 1 C can be stored in a fairly small volume, even though the capacitor/battery as a whole would be neutral.

To make things more difficult, let's say you want to store the charge in an isolated object surrounded by air at 1 atm. To keep the object from discharging into the surrounding air, the maximum E-field should be less than the breakdown field, which for air at 1 atm is about 3 kV/mm (this field can be lower at lower pressures). To minimize the maximum E-field, we can use a spherical conductor to store the charge. The E-field will be maximum at the surface of the conductor, given by

$$E_{max} = \frac{Q}{4\pi\epsilon_0 R^2}$$

where $$Q = 1\ \mathrm{C}$$ and $$R$$ is the radius of the sphere. We have

$$R>\sqrt{\frac{Q}{4\pi\epsilon_0E_{max}}}=54.7\ \mathrm{m}.$$

This is clearly a much smaller radius than that of the Earth, and since the sphere can be made hollow, you don't need nearly as much mass as that of the Earth.

I might be misinterpreting this question, in which case I apologize. Usually when people talk about storing charge, they're referring to capacitors. (Note: This is a bit of a misnomer. Capacitors don't store charge, they store energy, and the charge on a capacitor remains 0). If you're asking whether we can have a net 1 C charge on one plate of a capacitor, the answer is certainly yes. Though a 1F capacitor is overkill for the vast majority of practical applications, there's nothing that stops you from connecting a 1F capacitor to a 1V battery and creating a net charge of 1 C ($$Q = CV$$) on one plate. Such capacitors are certainly not 7 times the volume of the Earth.

The charge stored in a capacitor is given by :

$$Q = CV$$

Where $$C$$ is the Capacitance (units of Farad) and $$V$$ is the voltage across the capacitor. You can search available lists of capacitors you can buy and it's pretty easy to find a 1 Farad capacitor rated for 5 volts DC, which is capable of "storing" more than 1 Coulomb.

The part I found easily was an AVX(brand) SCMR18C105MRBA0.

Capacitors do store some charge and people working in electronics do need to be aware of the potential for lethal discharges from some capacitors. This certainly crops up when dealing with camera flashes, which use capacitors as a temporary buffer to store a large charge to create the flash with.

One teacher told me that to store 1Coulomb charge we need a material of about 7 times of Earth And another teacher told me that what he said was wrong who is correct

Not knowing the full context of what the first teacher we cannot say they are wrong, but you can certainly have a capacitor storing more than one coulomb.

Fora more mathematical answer, let's assume that for storing 1C charge you are using a parallel plate capacitor. Let it be connected across a very small potential difference of 1V (so as to maximize the capacitance C)

$$Q=CV \implies 1 = \frac{\epsilon_{0}A}{d} * 1$$. Where A is cross section area of capacitor and d is the distance between the parallel plates. $$\epsilon_{0}=8.85*10^{-12} F/m$$.

So if d=1000m (minimum value/separation that can be possible)(say), we would have $$A=1.13*10^{14} m^2$$.

Volume enclosed = $$Ad = 1.13*10^{17} m^3$$.

Radius of the Earth is $$R=6.4*10^6m$$.

Volume of the Earth(assuming it to be spherical) is $$4/3πR^3 = 1.098*10^{21}$$.

So it isn't the 7 times the size of Earth that you are asking, but it indeed requires a large volume to be stored.

Hence 1C of charge (or 1F capacitance) is a reaaaallly big value.

(Just image the force exerted by two point charges of charges 1C each by coloumb' s law)

The capacitance of a sphere is $$4\pi\epsilon_0 R$$. Plug in numbers for the earth and you get a capacitance of 0.0007 farad. With

$$C=\frac{Q}{V}$$

you need to raise the potential to about 1400 volts to store 1 coulomb. A sphere 7 times the volume of the earth would lower the voltage requirement to store that charge, but you don't say what the target voltage is to store the charge, so it is hard to know where the factor of 7 comes from.