Conductors, electrostatic pressure

1. Conductors, electrostatic pressure The external field exerts a force a surface of a conductor. The field generated locally by the surface itself obviously cannot exert a force (the sheet cannot exert a force on itself!). The force per unit area acting on the surface of the conductor (electrostatic pressure) always acts outward, and is given by:

2. s = + s Another way: let us move the small surface area by dl. The electric field is excluded from the region into which the conductor expands. The work done against the electrostatic force is

3. We have seen that an electric field is excluded from the inside of the conductor, but not from the outside, giving rise to a net outward force. We can account for this by saying that the field exerts a negative pressure on the conductor. We know that if we evacuate a metal can then the pressure difference between the inside and the outside eventually causes it to implode. Likewise, if we place the can in a strong electric field then the pressure difference between the inside and the outside will eventually cause it to explode. How big a field do we need before the electrostatic pressure difference is the same as that obtained by evacuating the can? In other words, what field exerts a negative pressure of one atmosphere (i.e., newtons per meter squared) on conductors? The answer is a field of strength E=108 V/m. Fortunately, this is a rather large field, so there is no danger of your car exploding when you turn on the stereo! Example: A soap bubble of radius R and surface tension T has been given a charge q. Find the excess pressure inside the bubble. The Young-Laplace equation: Thus the charge reduces the surface tension. the pressure difference across the fluid interface

4. Capacitors Any two conductors insulated from one another form a capacitor. A capacitor can be "charged" and can store charge. When a capacitor is being charged, negative charge is removed from one side of the capacitor and placed onto the other, leaving one side with a negative charge (-q) and the other side with a positive charge (+q). The net charge of the capacitor as a whole remains equal to zero. The amount of charge that can be placed on a capacitor is proportional to the voltage pushing the charge onto the positive plate. The larger the potential difference (voltage) between the plates, the larger the charge on the plates:

5. The constant of proportionality is called the "capacitance” Unit=Coulomb/Volt=Farad (1 F) Example: Parallel-plate capacitor Example: Spherical capacitor made of two concentric shells of radii a and b

6. The work to charge up a capacitor: Capacitors can be connected in a circuit in two ways, series or parallel (or combinations of series and parallel).