 Let's take a quick aside and discuss fields. Now mathematically a field is just something that has a value for each point of space. What kind of value? That's a kind of generic thing. Well the answer is any kind of value. It can even have units and different kinds of values for each point in space will define different kinds of fields. And you've met heaps of these. In a simple weather report we might see four or five different kinds of fields. So the first thing we might see is a temperature map. So that tells us the temperature all over the country. And any given point on this map is a particular color which specifies a particular temperature. So for every point in space on this map we have a temperature, mathematically that's called a temperature field. Well that might show us the pressure. So when you're talking about the weather it's really useful to know where the high and low pressure areas are. And so we have high atmospheric pressure here and they usually slap an H on it and they have low pressure over here. And that's really important in a weather report because where you've got high and low pressure areas it's going to have a strong effect on winds, it's going to have a strong effect on where rain clouds go and things like that. It's quite useful to use this contour map to show the pressure because you can really see there where the hills are in the high pressure and where the valley is for the low pressure. And what these contours are, a contour is a line where the pressure is the same. And so the pressure is the same all the way around there. And so it's higher as you go up. So this is a gradient as you go across the contour lines. You've got a gradient and so there you've got the pressure going up and here going into this low you've got the pressure going down. But all we're representing here is for each point on this map we have a value for the pressure. And so mathematically this is an example of a pressure field. So another really handy thing to learn when you're watching the weather is the wind and what you expect the wind to be and what it is now. And the wind of course has both a strength and a direction. And so something that has a magnitude and a direction is a vector. And if you want to show that the wind is different in different places you can draw different vectors all over this map. And so what we have here of course is just following the theme we have for each point in space a velocity. And so this is an example of a velocity field. So these two here, the temperature and the pressure are just a single number at each point in space. So the temperature is measured in Celsius or Fahrenheit or Kelvin and the pressure is measured in Pascals or atmospheres. And any physical quantity in physics that's described by a single number is called a scalar. And so these are scalar fields and the velocity is a vector field because we've got a vector at each point in space. And we can think of lots of other examples of these. So the volume of sound coming out of a speaker changes as you move around and so intensity might be a good scalar field. Density might be a really important one. If you're a geologist you really want to know where the dense rocks are and where the oil is. And so knowing the density field might be really useful. We've already met various vector quantities that changes you move around in space. Velocity of say wind might be one. Another might be the gravitational field. So we've already met the gravitational field and we know that things will accelerate differently whether they're close to or further away from other masses. And that's because they're experiencing a different force. And if the force changes in space then it must be a field. A key warning here is that if you say force field to a science fiction enthusiast then they're going to think you mean some kind of invisible barrier created by something akin to magic. Whereas if you say it to a physicist they're going to think you mean a force for each point in space. And so be very careful who you're talking to. Particularly if you're talking to a physicist who likes science fiction in which case you're just going to have to be very careful to communicate. So the idea of fields was actually introduced by Isaac Newton when he was describing gravity for the first time. And the concept was developed a lot more in the study of electromagnetism. And of course in this section we're going to be talking about electric fields and magnetic fields.