Potencial eléctrico
English
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개요
Fuente: Yong P. Chen, PhD, Departamento de física & Astronomía, Facultad de Ciencias, Universidad de Purdue, West Lafayette, IN
Potencial eléctrico, también conocido como “voltaje”, mide la energía potencial eléctrica por carga de la unidad. Campo eléctrico es una cantidad escalar y es fundamental para muchos efectos eléctricos. Como energía potencial, lo que es físicamente significativa es la diferencia de potencial eléctrico. Por ejemplo, la variación espacial en el potencial eléctrico está relacionado con el campo eléctrico, que da lugar a la fuerza eléctrica sobre una carga. La diferencia de potencial eléctrico entre dos puntos de una resistencia conduce la corriente eléctrica.
Este experimento utiliza un voltímetro y un tubo fluorescente para demostrar el potencial eléctrico (más exactamente, la diferencia de potencial entre dos puntos en el espacio) generado por una esfera cargada. El experimento demostrará el concepto de superficies equipotenciales, que son perpendiculares a los campos eléctricos.
Principles
Una carga punto Q situado en el origen (r = 0) produce un potencial eléctrico:
(Ecuación 1)
en cualquier punto en el espacio con una distancia r de la carga (en el origen r = 0). Ecuación 1 también describe el potencial eléctrico producido por una esfera uniformemente cargada (centrado en r = 0) con carga total Q en el espacio fuera de la esfera (figura 1). En ambos casos, el punto de “referencia” (donde el potencial es cero) está en la distancia infinita de la carga. El potencial eléctrico varía a lo largo de la dirección radial, que es la dirección del campo eléctrico.
Para dos puntos P1 y P2 con distancia r1 y r2 del origen (centro de la carga), respectivamente, la diferencia de potencial entre estos dos puntos es:
(Ecuación 2)
Si el punto P2 es en el infinito (→∞), esto reduce la ecuación 2 en la ecuación 1. Por lo tanto, hay una diferencia de potencial entre dos puntos y sólo si estos dos puntos tienen una distancia diferente del origen (centro de la carga). En este caso, una superficie esférica centrada en el origen es una “superficie equipotencial”. Nota en este caso, que el campo eléctrico (a lo largo de la dirección radial) es perpendicular a la superficie equipotencial (esfera). Esto resulta para ser generalmente cierto: la superficie equipotencial es perpendicular a la dirección del campo eléctrico.
Figura 1: Diagrama que muestra una esfera cargada conectada a un generador eléctrico. Se utiliza un voltímetro para medir el potencial eléctrico en un punto “A” (con la distancia r desde el centro de la esfera).
Procedure
Results
In steps 1.4-1.5, the voltmeter can be observed to give similar readings if the probe tip is kept at similar distances from the origin (that is, on an equipotential surface). However, the voltage drops if the probe moves farther away from the origin. The voltage reading at 1 m and 1.5 m away will be about 1/2 and 1/3 of the reading at 0.5 m away, respectively. If the voltage V measured versus the inverse distance (1/r) is plotted, a straight line results, as expected from Equation 1.
Applications and Summary
Electric potential (voltage) is ubiquitous and perhaps the most commonly used quantity in electricity. It is often much more convenient to use electric potential (which is a scalar) than electric field (which is a vector), even though the two can be related to each other. Electric potential difference is used to drive and control charge motion (accelerate/decelerate/deflect charges), for example in a TV screen or electron microscope. Electric potential difference (what we usually call voltage) is also what drives current flow in a conductor. Whenever one measures a voltage, one is measuring the electric potential difference between two points (one of which is sometimes a reference point or ground defined to have zero potential).
The author of the experiment acknowledges the assistance of Gary Hudson for material preparation and Chuanhsun Li for demonstrating the steps in the video.
내레이션 대본
Electric potential defines the energy of a charged particle. It gives rise to electric field and electric force, and is the basis of many electrical phenomena.
The term electrical potential is denoted by the Greek symbol Φ. It is a scalar quantity with a sign and magnitude. Any charge creates electric potential in the space around it. It is different from the term Voltage, although both these physical quantities are measured in Volts.
Here, we will first explain what these terms are, discuss the parameters that affect Φ, and then demonstrate the measurement of electric potential around a charged sphere.
As discussed in the Energy and Work video, potential energy of any object of mass m under the influence of gravitational acceleration g is equal to the amount of work needed to move that object by a height h from the ground. Mathematically, it is given by the formula mgh and has the unit of Joules.
Similarly, in the electric field E around a positively charged surface, the electrical potential energy at a specific point relative to a reference point is the amount of work necessary to move a positive test charge +q from the reference to that specific point. The distance between the two points is denoted by the letter d. Analogous to the gravitational potential energy, the electrical potential energy is the product of q, E, and d, and has the units of Joules.
Then, the electric potential or Φ at that point in the field is the electrical potential energy divided by ‘q’, the charge on the test charge. Therefore, the unit for Φ is joules per coulomb, AKA volts.
Now, if we consider another point in the field, it would have a different electric potential; say Φ0. The potential difference or Φdiff between the two points is known as voltage. This is the concept behind a battery, where the positive terminal is at a higher electric potential compared to the negative terminal and the difference between the two potentials is the voltage of the battery.
Coming back to electric potential, recall that it is a scalar quantity with a sign and magnitude. The sign depends on the source charge. Around an isolated positive charge, the potential is positive, whereas around an isolated negative charge it is negative.
The magnitude of the potential depends on the Q of the source charge producing the electric field, the distance d from the source charge, and the configuration.
For example, the electric potential at any given point around a point charge or a uniformly charged positive sphere with charge Q is given by this formula. It is evident that Φ is inversely proportional to the distance from the sphere. And the graph of electric potential magnitude versus distance is approaching zero at infinity.
This dependence on d also indicates that all locations at the same radius from the charged sphere would have the same potential. This means that there are equipotential surfaces of spherical shape around a charged sphere.
Now that we’ve explained the concepts behind electric potential and potential difference, let’s see how to validate these principles experimentally using a charged sphere.
This experiment uses a Van der Graff generator to charge a metal sphere. Connect the negative terminal of a voltmeter to the generator’s reference terminal or ground. Use a cable to connect the positive terminal of the voltmeter to a probe tip.
Turn the crank of the generator at least 10 times to charge the sphere then turn on the voltmeter and place the tip of the voltage probe about one-half meter away from the center of the sphere. Record the voltage reading at this location.
Move the probe tip around the sphere while maintaining a constant radius of one half meter from the center. During this time, observe the voltmeter measurements and note how the reading remains constant, indicating a spherical equipotential surface.
Repeat this procedure with the probe tip at a distance of one meter, and then one and a half meters from the center of the sphere.
The plot of measured potential versus distance displays a curve that decreases inversely with distance, which validates the theoretical relationship between electric potential and distance, for a charged sphere.
Electric potential is one of the most commonly used electrical quantities and is fundamental to the storage and release of electrical energy.
An electron microscope uses a high electric potential difference to accelerate electrons in a beam that bombards the sample under examination. These electrons act like a light in an optical microscope, but with much smaller wavelengths and much greater spatial resolution, enabling the ability to visualize sub-micron sized structures.
Electric potential is an important component of gel electrophoresis – a molecular biology technique commonly used for separating large molecules, such as DNA, by size and charge. In this technique, sample material is placed on a slab of agarose gel and an electric potential difference is applied between the ends. In the resulting electric field, the various molecules and molecular fragments move with speeds that depend on charge and molecular weight.
You’ve just watched JoVE’s introduction to electric potential. You should now know how to measure electric potential, and understand how it affects charges and relates to electric potential energy. Thanks for watching!