Gravitational & Electric Fields - A-level & GCSE Physics

gravitational and electric fields are very similar most of the equations we have to do with fields are the same for both of them but just slightly tweaked so what is a field a field is an invisible area in space if you put a mass or a charge in one of these fields gravitational and electric respectively then they will feel a force so let's say that I have a planet here if I put a mass in here near the planets which direction is the force going to pull of course it's going to be inwards and it doesn't matter where I put it force it's always going to be directed towards the planet because gravity is always attractive what about if I had a proton here though now if I had an electron then it would be attracted if I had another proton it would be repelled so which way do we put the field lines well they actually go outwards that's why field lines show the direction of the force on a point now when we say points we mean basically it has no volume itself show the direction of the force on a point mass so that makes sense I've got a point mass here force is pulling inwards but here are we talking about a point negative charge or positive charge well if a field lines are going away then we're talking about a positive charge we can call these point mass and charges test charges as well and test mass in other words with a point positive charge or a point mass we're testing the gravitational field here electric field here what I'm going to try and do is fit everything that you need to know for fields onto one piece of paper because everything fits together so well that it's not really that helpful to separate the ideas out too much so I'm going to be writing gravitational field equations in orange and electric field equations in blue so apologies if it gets a bit messy but let's start off with force what is the force felt by two masses that are separated by a distance R and when we talk about this separation we are talking about the separation of their centers not their surfaces because we treat these as point masses the force is given by Newton's law of gravitation that is F equals G that's the gravitational constant that's not acceleration due to gravity or gravitational field strength this capital G that is a universal constant G M M over R squared inwards force between two bodies is proportional to the product of their masses and inversely proportional to their separation the distance between their centers Newton's gravitational constant is in your formula sheet what about if we had two charges instead it's very very similar instead of the gravitational field constant we have this here this is 1 over 4 PI epsilon 0 epsilon 0 being the permittivity of free space it's just a constant again now because this whole thing here is a constant we can rewrite this as just k QQ over R squared then this K ends have been 9 times 10 to the 9 instead of having to put this into your calculator every time you can just put in 9 times 10 to the 9 and then carry on times and by the two charges and divided by the separation squared so you can see that they're very similar constant times the two masses times the 2 charges divided by R squared what about potential energy how its potential energy is there between these two masses here how do we get from force to energy well you should remember that energy or work done is equals to any Force Times distance moved so imagine that we've got these two imagine that these two masses were touching or rather their centers were touching and then we put in energy we put in work to separate them the distance R how is energy would that take that's going to be F times the distance but we're not talking D in this case because we're dealing with R so what happens we just times both of these equations by r so potential energy for gravitational fields is GM over R similarly for electric fields okay I'm just going to write k q Q over R don't forget that the force for a gravitational field can only be attractive but for electric fields it can be attractive or repulsive this is where it gets a little bit trickier what about if we had our planet again begin and we got our feel lines going in like that and I'm not going to put a second mass in here instead I just want to know how strong the field is at any given point in that case if I want to find out how strong the field is at any point I'm only dealing with or one mass the mass or the charge in electric field case that is producing the field to begin with so I'm effectively taking the second mess out of the equation so if I put it this way field strength is how much force would something feel so therefore I'm dividing by one of the masses for gravitational field strength and dividing by one of the charges for electric field strength and that gives me this here gravitational field strength we give the letter little G and you know from the earth that's 9.8 meters per second squared it's going to be G M over R squared see I've gotten rid of the little M similar for electric field strength unfortunately we do give it the letter capital e but it is a field strength not energy it's going to be KQ over R squared the unit for field strength is always Newtons per something for gravitational fields we're talking Newton's per kilogram for electric field strength yusin's per Coulomb so field strength just involves one mass or one charge the one that is producing the field to begin with and then all that field strength tells you is if you have something that was this far away how much force would it feel and it gives you the number of Newton's per kilogram or per Coulomb so if I had a field strength at this point here at 9.8 Newton's per kilogram yes it can also be meters per second squared because also known as acceleration due to gravity if I have 9.8 users per kilogramme that means that if I did have a kilogram of mass there it would feel 9.8 users if I had two kilograms there each kilogram is going to experience 9.8 Newton's so it's going to be double that nineteen point six and so on and so forth so if you have a field strength and you want to know what the actual force is not just the force per kilogram or Coulomb all you have to do is times by the second mass that you have in play or the second charge now there's a similar idea for energy as well instead of how much force would something feel in this case how much energy should something need so again we're dividing by mass and divided by charge to get to this new thing and whatever we've got is going to be equals to G ten over R same thing for electric field what is this call this potential we give that the letter V hang on a minute V potential potential difference yes it is exactly the same thing we have energy going to potential we know that voltage or potential difference is work done per unit charge that's what we've done we've taken our energy divided by the second charge to just get our potential how much energy said something need well the question is to do what the actual definition is to move from infinity to that point and it's going to be one kilogram or one Coulomb and that is the definition of potential it's the energy needed to move or one kilogram of mass it's a gravitational field or one Coulomb of charge this electric field from infinity to that point now you might realize that for a gravitational field you need to put in energy to move something further away so that's why we have a minus in front but that's not hugely important the important thing about potential is the change in potential the change in energy per kilogram or per Coulomb to move something from certain distance to another distance away we can draw equipotentials in other words drawn lines that show the same potential eques means the same equal so let's say that this line here represents a potential of minus 10 joules per kilogram this line here represents minus 4 joules per kilogram the important thing is knowing what happens when we move from one potential to the other in this case the change in potential is going to be 6 joules per kilogram if we know that then what we can do is times by the number of kilograms that our mass actually is to find out how much energy would be needed to do that so again to get from potential to actual potential energy all you have to do is times by the mass or the chance to get back now there is one more link you might realize that these equations are very similar to get from here to here you'll notice that to get from KQ over R to KQ over R squared all we have to do is divide by R so it turns out that field strength in both cases is merely the potential divided by the distance so that's why you can say that G is Delta V and for Delta R same thing for the electric field that's why field strength is also known as potential gradient in other words how does the potential change with distance so electric field strength is also known as potential gradient so we can be Newton's per Coulomb or volts per meter gravitational field strength also known as acceleration due to gravity can also be calculated doing potential to modify distance we don't give it the unit volts per meter though so I probably should just leave that in blue so hopefully you can see how all four of these things force potential energy potential and field strength all linked together force and potential energy require two masses or two charges field strength and potential are all about how much force would something feel how much energy would something need so they only need one mass or one charge the mass or charge that's creating the field to begin with these two these or we have to do is close by the second mass or charge just one most things sometimes you'll be given a graph of potential V against separation and you'll get this sort of shape there this can be for gravitational field or an electric field and because we know that field strength is changing potential with distance the gradient gives you G or e the field strength so you can find out the field strength at any point by taking the gradient at that point on the graph similarly you could get given a graph of field strength either one with distance it's the area under the graph gives you the potential so just a few more things let's say that we got two plates here and these are parallel plates and they're attached to something that is providing a PV of 10 volts so we have our voltage we have our potential difference in between we can know what distance these plates are separated by now say I have a charge in here Q I wanted to find out what force that this charge would feel in order to find out force I need my field strength times my charge I have this but I don't have field strength but like we said earlier on field strength is also known as potential gradient and that is the voltage the potential difference divided by separation D so let's say that this is two meters here then this is going to be ten volts divided by two we have a field strength of five Newton's per Coulomb once I got my field strength then I can times by my charge to find out what force that would actually be so there we go for parallel plates there's only ways for parallel plates you can take our voltage divided by the separation that gives us the field strength we know that if we have a planet then our field strength from the surface is proportional to one over R squared so it should have this shape here for what's going on inside of the planet it might surprise you to learn that the field strength increases linearly from the center so we would expect the field strength to be zero at the center because we have mass pulling in all directions but as we go further away it increases linearly that's because our field strength varies with R squared but we have a volume which is proportional to R cubed so ultimately this ends up being proportional to R it's really important anyone's doubt that you can have a resultant force and field strength in other words can be zero both force our field strength can be equals to zero let's say that we have a mass here and one and a second mass here and two and then we have a little mass in between and then separate by r 1 r 2 and if the mass is just sitting there and we know that the force between the two bodies here equals the force due to the two bodies here so at this point there is no resultant force same thing goes for their field strength as well at that point don't forget that we don't need that mass in order for the field strength to be zero just one thing to be wary of if we have two masses that are touching like we said we know that this separation is from this centers and sometimes what will happen is we'll have two bodies that are touching to begin with and then separated by another distance and it will seem like the separation has gone from zero to whenever the distance is not so the separation to begin with is the two radii of these masses added together and again just be careful that if instead you're given separation of their surfaces then you need to add on the radius of the bodies as well in order for the separation to be correct one last thing potential cannot be zero all right except at infinity this is always true for gravitational fields and electric fields so long this is only one type of charge present potential can be zero for example halfway in between a proton and an electron that's because the potentials are negative and positive equal the opposite so when you add them up they add up to zero so let's say that I have lots of positive charges and or producing their own electric field so here are some active potentials and for all of them now say I wanted to find out what the potential is at this point here there's a potential due to q1 potential due to q2 and a potential due to q3 if I know all of these distances here r1 r2 r3 how on earth will I find out the overall potential it's as easy as just adding them up so the potential at that point is the potential due to you q1 plus the potential due to q2 plus the potential GT q3 if you have any questions or suggestions then please leave it in a comment down below and I'll see you next time

Channel: Science Shorts

Views: 146,596

Rating: 4.9528198 out of 5

Keywords: unintended, 11th, lesson, technique, mark scheme, high school, grade, explained, entrance, college, questions, 10th, diploma, tutorial, naked, experiment, paper, revision, crash course, british, aqa, answers, edexcel, science, law, practical, university, soft, shorts, force, equations, 9-1, radius, sats, 1-9, 9th, english, lecture, gradient, investigation, strength, sat, fun, ap, spoken, placement, school, mcat, coulomb, exam, past, ocr, 12th, advanced, solutions, potential, homeschooling

Id: KfZIjNY7Cp0

Length: 16min 21sec (981 seconds)

Published: Tue Jul 18 2017