전위
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Overview
출처: 용피 첸 박사, 물리학 및 천문학학과, 과학 대학, 퍼듀 대학, 웨스트 라파예트, IN
“전압”이라고도 하는 전기 전위는 단전당 전기 전위 에너지를 측정합니다. 전기장은 스칼라 수량이며 많은 전기 적 효과의 기본입니다. 잠재적 인 에너지와 마찬가지로 물리적으로 의미있는 것은 전기 잠재력의 차이입니다. 예를 들어, 전기 전위의 공간 변화는 전위와 관련이 있으며, 이는 전하에 전기력을 초래한다. 저항기의 두 점 사이의 전기 전위 차이는 전류 흐름을 구동한다.
이 실험은 볼트 미터와 형광관을 모두 사용하여 충전된 구체에 의해 생성된 전기 전위(더 정확하게는 공간의 두 점 간의 잠재적 차이)를 보여줍니다. 이 실험은 전기장에 수직인 등구 표면의 개념을 보여줍니다.
Principles
원점(r = 0)에 위치한 포인트 충전 Q는 전기 전위를 생성합니다.
(방정식 1)
전하로부터 거리 r이 있는 공간의 어느 지점에서나(원산지 r = 0). 수학식 1은 또한 균일하게 충전된 구(r=0 중심)에 의해 생성된 전기 전위(r=0)에 의해 생성되는 전기 전위(도1)를설명합니다. 두 경우 모두 “참조” 점(전위가 0인 경우)은 전하와 는 무한한 거리에 있습니다. 전기 전위는 전기장의 방향인 방사형 방향에 따라 달라집니다.
원점(전하의 중심)에서 멀리 떨어진 거리 r1과 r 2의 2점 P1과 P2의 경우, 이 두 점간의 잠재적 차이는 다음과 이다.
(방정식 2)
점 P2가 무한대(→∞)에 있으면 방정식 2를 방정식 1로줄입니다. 따라서 이 두 점이 원점(전하의 중심)과 거리가 다른 경우에만 두 점 간에 잠재적 차이가 있습니다. 원점에서 중심의 구형 표면은 이 경우 “동등한 표면”입니다. 이 경우 전기장(방사형 방향)은 동등한 표면(구)에 수직이다. 이것은 일반적으로 사실로 판명 : 등구 표면은 전기 장의 방향에 수직입니다.
그림 1: 전기 발전기에 연결된 충전된 구를 보여주는 다이어그램입니다. 볼트계는 “A”(구의 중심에서 거리 r)에서 전기 전위를 측정하는 데 사용됩니다.
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!