Imagine that figure a represents voltage rather than height. Figure c shows some examples of ways to visualize field and voltage patterns. Top: A uniformly charged rod. Bottom: A dipole. In each case, the diagram on the left shows the field vectors and constant-voltage curves, while the one on the right shows the voltage up-down coordinate as a function of x and y.
Interpreting the field diagrams: Each arrow represents the field at the point where its tail has been positioned. For clarity, some of the arrows in regions of very strong field strength are not shown they would be too long to show. Interpreting the constant-voltage curves: In regions of very strong fields, the curves are not shown because they would merge together to make solid black regions.
We therefore look at a uniform electric field as an interesting special case. The work done by the electric field in Figure 1 to move a positive charge q from A, the positive plate, higher potential, to B, the negative plate, lower potential, is. Note that the above equation implies the units for electric field are volts per meter.
Dry air will support a maximum electric field strength of about 3. Above that value, the field creates enough ionization in the air to make the air a conductor.
This allows a discharge or spark that reduces the field. What, then, is the maximum voltage between two parallel conducting plates separated by 2. We are given the maximum electric field E between the plates and the distance d between them.
One of the implications of this result is that it takes about 75 kV to make a spark jump across a 2. This limits the voltages that can exist between conductors, perhaps on a power transmission line. A smaller voltage will cause a spark if there are points on the surface, since points create greater fields than smooth surfaces.
Humid air breaks down at a lower field strength, meaning that a smaller voltage will make a spark jump through humid air. The largest voltages can be built up, say with static electricity, on dry days. Figure 2. A spark chamber is used to trace the paths of high-energy particles. Ionization created by the particles as they pass through the gas between the plates allows a spark to jump. The sparks are perpendicular to the plates, following electric field lines between them.
The potential difference between adjacent plates is not high enough to cause sparks without the ionization produced by particles from accelerator experiments or cosmic rays. For this example of a constant electric field, I can solve for the magnitude of the electric field in terms of the change in potential. Although this expression is only true for a constant electric field, it's still useful.
This says that the electric field doesn't depend on the electric potential but rather how that potential changes with distance. How about an analogy? Suppose you have a ball on a hill. If you let go of the ball it will start to roll down the hill and the acceleration of the ball depends on the steepness of the hill. This ball acceleration is like the electric field. The height of the hill would be like the electric potential.
Which ball is higher? Yes, the answer is A. Which ball will have a greater acceleration? The answer is ball B—even though it's not as high as ball A, the hill is steeper there. I'm using this to address a very common electric potential problem. Consider the following two cases:.
You might think these two locations would be in the same place—and that is possible. However, they don't necessarily have to be the same.
Let's go back to the hill example. What if there was a location where the height above sea level was zero meters. Would that mean the slope would have to be flat? It could be a beach sloping into the water and not completely flat. What if the hill was flat, does that mean the height of the hill is zero?
Think about the top of a hill that's flat—that's possible. Again no. The electric field depends on the spatial rate of change technically called a gradient of the electric potential. It does NOT depend on the actual value of the potential. These have a couple of very useful features. We can use this to show the connection between electric field and electric potential.
Here's how it starts. I'm going to take this shallow plastic tray and add water with a little bit of salt to make it an electric conductor. On the ends of the tray I will add two strips of aluminum foil that are connected to a power supply with the positive terminal to one side and the negative on the other. Because of the aluminum foil on the sides, there is a roughly constant electric field in the water going from one side to the other.
This electric field also creates an electric current in the water. The LED is mounted on the top of the brick with the two leads connected to wires on each side to serve as the person's legs. What is a Van der Graaf generator? How do lightning rods serve to protect buildings from lightning strikes? Why is the electric field inside a conductor zero? How does permittivity affect electric field intensity?
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