Let us see how they can be focused by a magnetic field. Figure shows an electron gun situated inside a long solenoid. The electrons that emerge from the hole in the anode have a small transverse velocity component and, if there is no current in the solenoid, they spread out as in the figure. Let us see what happens when we turn on the magnetic field.

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For any surface S bounding a volume t. The net charge density inside a homogeneous conductor carrying a current under steady-state conditions is zero.

For ordinary conductors, Ohm's law applies: 5. The electric charge density inside a uniform current-carrying conductor is zero under steady-state conditions. Other resistors are said to be non-linear. The resistance of a set of resistors connected in series is equal to the sum of their individual resistances. The conductance of a set of resistors connected in parallel is equal to the sum of their individual conductances. The principle of superposition states that, as long as all the resistors in a circuit are linear, each source acts independently of the others and produces its own set of currents.

Kirchoff's current law states that the algebraic sum of the currents entering a node, in an electric circuit, is equal to zero. His voltage law states that the sum of the voltage drops around a mesh is equal to zero. Currents in the various branches of a circuit are usually calculated by using mesh currents and the voltage law.

One can transform the delta-connected circuit of Fig. Thevenins theorem states that any source may be represented by an ideal voltage source, in series with a resistance called its output resistance. When a source is connected to a circuit comprising capacitors, transient currents flow temporarily in the circuit until all the capacitors are charged.

Neglect edge effects. The current density is J. Find the electric field intensity in the conducting plate, as a function of the dis- tance x from the positive electrode. Show that the resistance between the electrodes depends only on the thickness of the film and on its conductivity, as long as the film is square.

This resistance is given in ohms per square. Nichrome films range approxi- mately from 40 to ohms per square. See also Probs. The propellant gas P is admitted on the left, heated to a high temperature by the resistor, and exhausted through the nozzle.

See Prob. Assuming complete conversion of the electric energy into kinetic energy, calcu- late the thrust for an input power of 3 kilowatts and a flow of 0. What is the maximum voltage that can be applied across it? The voltage on R2 and R is V0. The circuit is used in strip-chart recorders.

In that case the current 7 is amplified to actuate the motor that displaces the pen, and simultaneously moves the tap on the resistance in a direction to decrease 7. This is one type of servomechanism. We shall use this result in Prob. The circuit is so widely used today that it is almost impossible to list all its applications.

Some of the better known are the following. If one of the resistors is a temperature-sensitive resistor, or thermistor, the bridge serves as a thermometer, V being a measure of the temperature. If one of the resistors is a temperature-sensitive wire, heated by the bridge current and immersed in a gas, V is a measure of the gas velocity, or of its turbulence.

One then has a hot-wire anemometer. In the Pirani vacuum gauge the heated wire is in a partial vacuum and is cooled more or less by the residual gas, according to the pressure. In certain gas analyzers, the heated wire is exposed to the unknown gas. Then V is a measure of the thermal conductivity of the gas. Such analyzers are used, in particular, for carbon dioxide. The thermal conductivity of carbon dioxide is roughly one half that of air In flammable-gas detectors the wire is heated sufficiently to ignite a sample of the gas contained in a small cell.

The heat generated by the combusion increases the temperature and changes the resistance of the wire. The deflection of the volt- meter pointer is a measure of the flammability.

If one of the resistors is a fine wire whose resistance changes when elongated, the bridge serves as a strain gauge for measuring microscopic displacements or deformations. If the strain gauge is attached.

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## Woldemar Voigt

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## paul lorrain dale corson eletromagnetismo

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