# Electric field of a charged object

1-The Lorentz Force Law states that $F=q(E+vB)$. Therefore, let's say that we have a point charge with charge $q$. If we want to calculate the force exerted by a charge $q_1$ on another charge $q_2$ located at a distance $d$, we can calculate it with Coulomb's Law which is $F=\frac {q_1q_2}{4\pi \epsilon_0 d^2}$. Then, for calculating the electric field exerted by this point charge, we can use Lorentz Force Law. Assuming that the point charge is not moving, (velocity equal to zero) and there is no magnetic field exerted by it, the electric field would be: $$E=\frac Fq=\frac {q_2}{4\pi \epsilon_0 d^2}$$ Thus the electric field is inversely proportional to the distance between the point and the point charge. Then does all charges, no matter how much charged are they, ionize the material around them since distance can get smaller and therefore electric field gets bigger. Consequently, the electric field exerted by the charge would be higher than the electrical breakdown limit of the material around it. This also works with any kind of shape since the electric field that they exert can be calculated by integration.

2-My other question is more basic. When we try to calculate the electric field between a capacitor which has two oppositely charged object, object charged with negative sign would exert a negative electric field whereas object charged with positive sign would eert positive electric field. If the amount of charges were the same in each object, would the positive electric field and negative electric field cancels out each other and would the net electric field be 0? I know it doesn't work like that but I want to get the correct information.

Then does all charges, no matter how much charged are they, ionize the material around them since distance can get smaller and therefore electric field gets bigger. Consequently, the electric field exerted by the charge would be higher than the electrical breakdown limit of the material around it.

Let's say you magically stick a (positive) charge inside a piece of material. You can imagine getting as close to a charge as you want, but the "material around it" is still made up of atoms which are a certain distance away. The atoms of the material are not a continuum which gets infinitesimally close to your charge. The electrons of the material may get close, but you have to think of the electrons quantum mechanically: they are "smeared out" in space, and to avoid getting into that here, the small region where the electric field is arbitrarily high gets averaged out from the point of view of the smeared electron.

2-My other question is more basic. When we try to calculate the electric field between a capacitor which has two oppositely charged object, object charged with negative sign would exert a negative electric field whereas object charged with positive sign would eert positive electric field. If the amount of charges were the same in each object, would the positive electric field and negative electric field cancels out each other and would the net electric field be 0? I know it doesn't work like that but I want to get the correct information.

You have to consider not just the magnitude, but also the direction of the electric field. Say the positive charge is above and the negative charge is below. The positive charge creates an E-field pointing away from itself, so, inside the capacitor, that points downward. The negative charge creates an E-field pointing towards itself, so, inside the capacitor, that points downward. Thus both E-fields actually add together to make a stronger one. If you play the same game but outside the capacitor, you'll find the E-fields cancel each other (all of this assuming you do the standard infinite capacitor plate).

• Thanks for your answer. I understood what you are saying but how does it work if we don't consider it quantum mechanically. Let's say we have a charged object which exerts an electric field that is not higher than the electrical breakdown limit of medium at a point 1 meter away from the object. Wouldn't it ionize the air at the point which is 1 cm away(not infinitesmally distance like electron's size) from the object? If this is true then wouldn't we see the effect of ionization of air because of electric cables that we see high ground since charges are flowing in them? – Starior Dec 14 '14 at 19:38
• 1) Yes, if you had a really charged object, it could break down the air around it, creating sparks. Note though, that these sparks discharge your object. 2) But also, remember that the electric wires are charge neutral. Ie, they have negative charges flowing through them, but there are also the positive charges from the nuclei of the wires. The net effect is that, outside the wire, we don't see strong static electric fields. – Sam Bader Dec 14 '14 at 19:50
• Then how do electricians know if a charged object or wire would cause damage to objects around it?(For example in power stations) Is there a way to calculate the maximum amount of charge that an object can have for that not to happen? What electric field would be safe? For example, the electrical breakdown limit of air is 3*10^6 V/m. Since the electric field is not constant that an everyday object exerts what distance should be taken to calculate if its electric field is higher than the electrical breakdown limit? – Starior Dec 14 '14 at 20:03
• The thing is, electricians generally don't deal with charged objects. They deal with wires carrying currents, and these wires have the same number of electrons flowing through them as nuclei in them, so there is no net charge. Separating positive and negative charges takes energy to do, so most objects are, when taken as a whole, pretty close to neutral. – Sam Bader Dec 14 '14 at 20:25
• To answer your second question about what distance needs to be taken to see whether an object will break down the surrounding air...Since everyday objects are huge compared to the spacing of air molecules, if you're interested in breakdown due to an everyday-sized object, you can basically treat air as continuous and calculate the field arbitrarily close to the object. Ie for the Van de Graaff generator I linked to before, you can calculate the E-field at the surface of a hollow charged sphere and compare that to the breakdown voltage of air. – Sam Bader Dec 14 '14 at 20:25

Electricity is neither positive or negative as that is just a phrase attempting to explain it and is wrong ! To fully understand electricity we need to view it as a vacuum where positive is a gain in pressure and negative as like an empty void with space between them ! Here we consider space as time and the rate of charge is time over space !

Volts is the measure of time it takes for a charge or a change in pressure to complete as to form a point of unity ! If say you have a load like a light bulb the light bulb is in fact converting the pressure change and emitting it away as heat and light ! There is in fact no such thing as attraction between a positive or a negative as they are in fact falling together rather than being pulled together ! In a conductor say a coil there are free standing electrons between atoms and are there because of a point of over charge when they were born in a super nova and cooled very quickly. But you can increase the amount of free standing electrons if that is required but only I know how to do that.

So for now lets look again at the result between a negative pressure and a positive pressure with a conductor in the middle. The free electrons inside the conductor when connected to the positive pressure and the negative pressure experience compression due to a movement between the two points of pressure. This brings the free electrons closer together and there event horizons that are spinning at 5.5 million mph start to interact causing the to release the gain in field pressure ! Each free electron has its own field that protects it from other electrons and this field also has a physical construct known as the magnetic field but lets just for now look at the change on pressure !

You may thing that positive and negative are attracting each other into the conductor but they are only trying to find a point of EQ a balance between them ! But the real reason they move towards each other is the space between them is collapsing resulting in the creation of time ! Know as the space time continuum ! The cause of the collapse of space between these two points of pressure is due to there speed of change not there attraction . When an object is moving close to the speed of light it will create a change in the space time continuum equal to the pressure between positive and negative and now we have a 4rd construct included in the equation. So we now have positive pressure negative pressure the resistance of the free electrons as the conductor and TIME .......

Time is like water inside a negative cup the cup is empty and creates a vacuum for time to sit inside and a positive pressure is a cup full of flux. If a pipe was connected between the two and a tap opened permitting flow than both cups become neutral zero pressure. But the rate and speed of this exchange can not exceed the speed of light so time is what keeps this reaction at or below the speed of light ! Take away time in the equation the rate and speed would be so great the pipe would explode at an equal amount of energy as there is in the universe. We don't want that to happen hahah ! So time steeps in and keeps it all at a safe point of conversion!

No funny maths here is there, and no other laws at play and if there is an over charge than the space between the negative and positive pressure in the atmosphere will also collapse causing sparks hahaha ... Again this is due to time or the collapse of time !

The 2 cups represent 2 electrons and they are pulled together from the emitting conductor and its speed of reaction is kept constant by time ! Time will make the free electrons in between the 2 cups heavier and there for at the constant of the speed of light . So now we value time as gravity and equal to the mass within it ! The more the mass the slower the time the more the charge the more time is created and the heavier the mass becomes!

So the truth is simple when we include time ! And now we value time as neutral and constant energy and it is proven by that very fact that the universe is here. So next time you attempt to value electricity remember that with out time there would be no electricity.

• Excuse me, what? None of this makes any sense. – Hritik Narayan Nov 17 '15 at 12:28
• Next time, you attempt to write an answer, make sure you read the question before doing so. – SchrodingersCat Nov 17 '15 at 13:23