Potenziale elettrico
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Overview
Fonte: Yong P. Chen, PhD, Dipartimento di Fisica e Astronomia, College of Science, Purdue University, West Lafayette, IN
Il potenziale elettrico, noto anche come “tensione”, misura l’energia potenziale elettrica per unità di carica. Il campo elettrico è una quantità scalare ed è fondamentale per molti effetti elettrici. Come l’energia potenziale, ciò che è fisicamente significativo è la differenza nel potenziale elettrico. Ad esempio, la variazione spaziale del potenziale elettrico è correlata al campo elettrico, che dà origine alla forza elettrica su una carica. La differenza nel potenziale elettrico tra due punti in un resistore guida il flusso di corrente elettrica.
Questo esperimento utilizzerà sia un voltmetro che un tubo fluorescente per dimostrare il potenziale elettrico (più precisamente, la differenza di potenziale tra due punti nello spazio) generato da una sfera carica. L’esperimento dimostrerà il concetto di superfici equipotenziali, che sono perpendicolari ai campi elettrici.
Principles
Una carica puntica Q situata all’origine (r = 0) produce un potenziale elettrico:
(Equazione 1)
in qualsiasi punto dello spazio con una distanza r dalla carica (all’origine r = 0). L’equazione 1 descrive anche il potenziale elettrico prodotto da una sfera uniformemente carica (centrata a r = 0) con carica totale Q nello spazio esterno alla sfera (Figura 1). In entrambi i casi, il punto di “riferimento” (dove il potenziale è zero) si trova alla distanza infinita dalla carica. Il potenziale elettrico varia lungo la direzione radiale, che è la direzione del campo elettrico.
Per due punti P1 e P2 con distanza r1 e r2 di distanza dall’origine (centro della carica), rispettivamente, la differenza di potenziale tra questi due punti è:
(Equazione 2)
Se il punto P2 è all’infinito (→∞), questo riduce l’equazione 2 all’equazione 1. Pertanto, c’è una differenza potenziale tra due punti se e solo se questi due punti hanno una distanza diversa dall’origine (centro della carica). Una superficie sferica centrata all’origine è una “superficie equipotenziale” in questo caso. Si noti in questo caso, il campo elettrico (lungo la direzione radiale) è perpendicolare alla superficie equipotenziale (sfera). Questo risulta essere generalmente vero: la superficie equipotenziale è perpendicolare alla direzione del campo elettrico.
Figura 1: Diagramma che mostra una sfera carica collegata a un generatore elettrico. Un voltmetro viene utilizzato per misurare il potenziale elettrico in un punto “A” (con distanza r dal centro della sfera).
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.
Transcript
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!