 We have defined electric field strength as the amount of force acting on a coulomb of charge force per coulomb So Newton's per coulomb right now in this video We will look at a new way of defining electric field strength in terms of potential difference So let's let's start by something that we already know. Let's use this definition So let's take an example imagine we have a uniform electric field towards the right created by some sheet of charge Let's say and let's say that strength is hundred Newton's per coulomb Let's start by asking ourselves. What is the meaning of this statement according to this definition? Well, it basically means that if I keep a hundred or sorry a coulomb of charge in That electric field anywhere. It's uniform and that coulomb would experience hundred Newton's of force hundred Newton's per coulomb Similarly, what would mean if I had let's say another electric field say upwards and let's say this electric field was 500 Newton's per coulomb. What were the meaning of that? Well, this would mean over here if I now bring that one coulomb of charge and keep it over here and that coulomb would experience 500 Newton's of force 500 Newton's per coulomb Okay, now let's think of this in a different way and for that here's my question to you Imagine I let go of this charge. So I keep my charge over here. I'm holding it right now Let's say let go of that charge. What's gonna happen? Well, it's it's experiencing a force towards the right and so it'll accelerate towards the right and as it does that It's gonna gain speed. It's gonna gain kinetic energy as it goes towards the right, which means it's gonna lose Potential energy. It's just like a ball falling down as it gains speed. It loses potential energy, right? So that means as it goes forward it gains kinetic energy. It loses potential energy what I want you to try and figure out is how much potential energy this coulomb of charge would have lost if It went forward or when it goes forward by exactly one meter So can you pause and calculate? How much potential energy it would lose by the time it would have traveled exactly one meter? So, can you pause and try and figure this out? All right, let's see. So let's start by asking ourselves. How do we calculate how much potential energy is lost or gained? Well, that is calculated by the work done. The potential energy lost or gained is the work done by the electric field And so how much is the work done over here? So the work done over here? Let me write that. Let me write that somewhere The work done over here is Force into displacement hundred into one. That's a hundred joules Hundred joules and that work is done for one coulomb of charge So work done is hundred joules per coulomb and that means this coulomb will lose Hundred joules of potential energy by the time it travels one meter. Does that make sense and all of that hundred joules will get converted into kinetic energy Another way of saying that is we can say as I go forward by one meter. We will lose hundred joules hundred joules Per coulomb hundred joules of potential energy per coulomb meaning hundred walls Joules per coulomb is also called walls. So let me let me raise that and let me write this as walls Hundred walls as I go forward one meter. So I could say a hundred walls per Meter does that make sense? Think about it For every meter that I travel forward. I would lose hundred walls of potential in this electric field Okay, now similarly, what can you say about this electric field? How many how many walls would we lose if you go one meter forward? All right Well, it's good. The calculation would be very similar if I go one meter forward So let's say this is one meter The work done by the electric field would be 500 joules. So 500 joules per coulomb So 500 volts for every meter you go forward. So in this electric field We will lose 500 volts much higher 500 volts per meter And this is our new way or new definition of our electric field strength So our electric field this number is telling us how much potential gets dropped for every meter You go forward along the field Okay, and so now let me move this a little down Okay, let me move this over here. All right So now we can also say that this electric field Equals a hundred Instead of calling it newtons per coulomb. I can also say volt 100 volt per meter And what does it mean when I say electric field is 100 volt per meter It's saying that in this field for every meter you go forward. You lose 100 volts Similarly, I can now write this as I can now write this as 500 500 volt per meter Although there is a volt over here. This is not potential. This is field volt per meter And what is this saying? This is saying oh, this is a much stronger field For every meter you go forward. You lose 500 volts of potential So what's our new way of defining electric field strength? We can say it is a measure of how much potential drops potential Drops per meter Per meter as you go forward in the electric field. Okay, and how do we write that mathematically? So let me write that over here. How do we write this mathematically? We could say electric field equals potential drop which we can write as delta v Per meter which we can write as per distance So per delta r or delta x. What do we want to call that? Delta r or delta x and what's the unit? It's volts per meter. So a new way of looking at electric field Now one thing we need to be very careful. This is not complete equation yet One thing to be careful is remember The number is saying how much potential you're losing as you go forward. Remember it's a drop Okay, and how do we take care of that in the mathematics mathematically when we write it If I just write delta v it represents how much potential is gained because it's a positive number But we are saying it's the how much potential is lost and it's for that reason we put a negative sign over here So the negative sign Is basically saying it's a measure of how much the potential drops Think of it this way If your electric field, let's say is positive Yeah, let's say right side is positive if your electric field was positive And let's say you also move in the positive direction delta r is also positive What would happen to your potential would you gain or would you lose? You're losing. That's what we're saying. You're losing and therefore this needs to be negative So it's saying that if both these are positive the delta v has to be negative and therefore that's why we have a negative sign And of course in the future video we'll lose also numericals and this will make more sense But long story short electric field is a measure of how much potential gets lost for every meter you go forward Now before we conclude there's one Last thing I want to mention of how do we write this? You know, how do we say this technically? So whenever you're calculating how much something is changing How much something is changing with respect to distance? Or how much something is changing per meter? We give it a name. We call that a gradient. So let me write that This is called gradient. Okay. So if I said something like Temperature gradient, it means it's a measure of how much temperature is changing for every meter you go forward So this is potential gradient because it's a measure of how much potential is changing for every meter you go forward So our right hand side is potential gradient. Um, let me Let me shift this. Sorry this little little space. Let me try and make this so this whatever we're writing Whatever we're calculating is potential gradient A potential gradient And therefore we can now say that electric field. This is what you will see in your textbooks Electric field is the negative potential gradient. If I just say potential gradient, it means how much it's increasing So I have to say how much it's decreasing how much potential is decreasing and so We can now say electric field is A negative potential gradient sounds very cool to say that but hopefully now this makes a lot of sense Basically means how much potential is losing for every meter you go forward