Electric Field: Part 1

Excerpts from http://www.alevelphysics.info/

Here, we look at what electric field is about. This is, unfortunately, not the most familiar type of electricity in every day life. We are more familiar with electrical voltage and current. When we switch on the television, we are allowing electric current to flow through the wires into the TV. What flow through the wires are electrons. These are tiny particles that are much smaller than atoms, and much lighter. Throughout the topic on electricity, we shall be exploring the effects of these little particles.

Now, imagine getting two small, light plastic balls. Tie a string to each one and hang them side by side, close to each other. Get a piece of cloth, rub the balls, and release them. If you are lucky, you will see the balls move away from each other. I say 'lucky', because it is not always easy to get it right. Everything must be very dry, and it may not work for some type of cloth or plastic.
On this page, we want to understand a little bit more about why these two balls move apart. What happens when you rub a ball is that you are rubbing off some of the electrons from the ball. You may also be rubbing extra electrons into the ball, depending on the cloth or ball. For now, lets assume that the cloth actually removes some electrons from the ball.

Normally, each atom in the ball is made up of the same number of protons at the centre, and electrons around it. When some electrons are rubbed away, from the ball, we end up with slightly more protons. When both balls are short of electrons, they can push each other away, as we have seen. Somehow, there is a force that goes through the air from one ball to the other ball and pushes it. This force is called an electric force.

There must be something in the protons and electrons that gives rise to this force. We cannot see it, but scientists have done a great deal of experiments on it and found about a lot about how it behaves. They have given it a name - the electric charge. What they found is that, we can think of each electron as having a charge. This charge is a quantity like mass, but it has no weight. It is another aspect of the electron, just like mass and colour are two different aspects of a ball. Like mass, we can talk about the amount of charge with a number. The unit of mass is kilogram. The unit of electrical charge is Coulomb.

The funny thing about charge is that, it can be a positive number or a negative number. Electrons have negative charge, but protons have positive charge. Before you rub the ball, the is the same number of electrons and protons in the ball, so the total charge is zero. When you rub off some electrons, you have slightly more protons. The the total charge is slightly positive. As you have seen, two positively charged balls push each other away. That is, they repel each other.

If we use a different type of ball and cloth, say wood and fur, we may be able to rub electrons into the ball. Then we have more electrons than protons, and the ball becomes negatively charged. If you hang a positively charged ball next to a negatively charged ball, you will see that the come closer together. That is, they attract each other. The scientists have checked this very carefully, that is why they came up with this idea of using negative numbers for the charges to explain the oppositve direction of the force - attraction is opposite to repulsion.

We have now set the scene for what we need to learn. On a forthcoming page, we shall see how the idea of an electric field grows from this.

Velocity-Time Graph: Displacement

Excerpts from http://www.alevelphysics.info/



In this section, we are going to learn how a velocity- time graph can tell us the displacement of an object. Now both velocity and displacement have directions. This can make things complicated. So to make it easier to learn about this, lets just think about them like speed and distance, and ignore the direction at first.






Lets look at this speed-time graph and think about how it can tell us what the distance is. The graph tells us that the object, whatever it is, moved at the speed of 2 m/s for a time of 3 s. Once we are clear about this, we don't really need the graph any more. Just use:

distance = speed x time

So distance = 2 x 3 = 6 m. Simple. Now lets take a look at the graph again. Can you see a rectangle under the graph (line)? The height of this triangle is 2, and the base is 3. 2 x 3 happens to be the area of this rectangle. With some imagination, you can see that the distance is always equal to the area under this graph, even if the speed and time are different. This is assuming, of course, that the speed remains the same.

What if it does not. Suppose the speed increases with time like this.

The graph goes up in a straight line. We say that the speed increases uniformly. Every second, the speed increases by the same amount. How are we going to find the distance in this case? You see the triangle under the graph (slanted line)? I am going to ask you to take a leap of imagination now, and tell you that the distance is the area of this triangle.

This is not so easy to understand as the rectangle earlier. Unfortunately, I am going to have to ask you to just accept it, as the reason is not covered in A level physics. We can still learn to use the idea anyway. So lets find this area. The area of a trangle is given by the formula

area = 1/2 x base x height

Therefore the distance = 1/2 x 3 x 2 = 3 m.
Now that we are quite comfortable with finding distance from the area, let us now move on to full fledged velocity and displacement. Lets make life more difficult and put in the direction.

Lets look at the familiar example of a ball rolling up the slope, and the velocity-time graph that looks like this.

We need to think about finding displacement from this graph. Lets start with the easy bit. Lets look at the part of the graph between 0 and 2 s. On this part of the graph, the velocity has + sign. As long as the ball is going in the same direction. we can treat it as a simple speed-time graph, and not worry about the direction. Then we can find the distance by finding the area in the triangle between 0 and 2 s. That would be

area = 1/2 x base x height = 1/2 x 2 x 2 = 2 m

This tells us that the displacement of the ball is +2 m, or 2 m up the slope.
Next, we turn our attention to the time from 2 to 4 s. Since the velocity here has - sign, it means the ball is rolling down the slope. That is the job of hte - sign, to tell us the direction. Since it is going in the same direction during this time from 2 to 4 s, we can find the distance from the area. If you are quick to notice this area is symmetrical with the area from 0 to 2 s, then you already have the answer. It is 2 m. So the displacement is -2 m, or 2 m down the slope.
Lets summarise:

0 to 2 s, displacement is +2 m

2 to 4 s, displacement is -2 m

So what is the displacement from 0 to 4 s? If you think that it is zero, then you are right. 2 m up, 2 m down, the ball is back where it started.
Tip: No matter how the ball moves over a period of time - up, down, left, right - the displacement is the straight line distance from start point to end point, and the direction is the direction of this straight line.

About me

Excerpts from www.alevelphysics.info

My name is Kai Meng. I grew up in Singapore, a small island country in South-east Asia. It is just 1 degree north of the equator, so you can imagine that it is very hot. I spent most of my childhood eating chicken rice and durians, two of the most famous food there. Somehow, I got very interested in physics at the age of ten. The interest stayed with me all my life. When I was 19 years old, I came to England and studied physics at Cambridge University. I had the most enjoyable time. I stayed for 7 years and did both my BA and PhD degrees. This is a photo of Gonville and Caius College, my college in Cambridge, and a photo of Cavendish Laboratory, where I learnt a lot of physics.


Caius College (courtesy of rossgoesabroad.blogspot.com)


Cavendish Lab (courtesy of www.phy.cam.ac.uk/alumni/)

After graduation, I went back to Singapore and worked as an engineer for 14 years. At the age of 40, I came back to England to do research in physics. I am currently doing a postdoc in accelerator physics. I do calculations that help in the design of the the International Linear Collider. This will be a huge accelerator that hopes to answer some very fundamental questions, like how the universe started. If you are interested, you can find more information here: www.linearcollider.org

If you have any feedback or suggestion, I shall always be happy to hear from you.