Umair Gaines
Electric potential, also known as voltage, is a scalar quantity that is simpler to evaluate than an electric field. It is the potential difference between two points that is of importance, with one reference point often assumed to be at zero potential. This reference point could be Earth or a distant point. The electric field inside a conductor is zero, and the potential in the interior of the sphere is identical to that on the surface. In magnetism, charges moving in a magnetic field are subject to a force that moves them, and when charges move, potential differences are created. This is a consequence of Maxwell's equations, which state that a changing magnetic field produces an electric field, and a changing electric field produces a magnetic field. The magnetic vector potential, along with the electric potential, can be used to specify the electric field.
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What You'll Learn
Electric potential difference
Voltage is often compared to pressure difference in a water circuit, where a pump creates a pressure difference between two points, allowing water to flow and do work, such as turning a turbine. Similarly, in an electric circuit, the voltage provided by a battery creates a potential difference, enabling electric charges to move and power devices.
The unit of measurement for voltage is the volt (V), and it can be measured using a voltmeter. It is important to note that the choice of zero volts is arbitrary, similar to how sea level or the floor of a lecture hall can be arbitrarily chosen as the zero reference point for gravitational potential energy.
The relationship between voltage and energy is important to understand. While they are related, they are not the same thing. For instance, a motorcycle battery and a car battery can have the same voltage but supply different amounts of energy. This is because voltage represents the energy per unit charge, so the battery with a larger capacity will be able to move more charge and supply more energy.
The electric potential difference is also essential in understanding the behaviour of charged particles in magnetic fields. The presence of a magnetic field can increase or decrease the potential difference, influencing the movement of charged particles. This change in potential difference can be calculated using the electric potential difference between the starting and ending points of the particle's path.
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Magnetic vector potential
In classical electromagnetism, the magnetic vector potential, often denoted as 'A', is a vector quantity defined so that its curl is equal to the magnetic field, B. The magnetic vector potential can be used alongside the electric potential to specify the electric field E. This means that many equations of electromagnetism can be written in terms of the fields E and B, or in terms of the potentials and A.
In the context of special relativity, it is common to combine the magnetic vector potential with the (scalar) electric potential to create the electromagnetic potential, also known as the four-potential. This is done because the four-potential is a mathematical four-vector, and using standard four-vector transformation rules, the electric and magnetic potentials can be calculated in any inertial reference frame.
The magnetic vector potential was introduced by Franz Ernst Neumann and Wilhelm Eduard Weber in 1845 and 1846, respectively, to discuss Ampère's circuital law. William Thomson introduced the modern version of the vector potential in 1847, along with the formula relating it to the magnetic field.
The vector-potential method can be used to find the magnetic field of a small loop of current. By taking the curl of the vector potential, we can obtain the magnetic field. The principle is that the x-component of the vector potential arising from a current density is the same as the electric potential that would be produced by a charge density equal to jx/c^2.
The choice of a particular function or constant is referred to as a choice of gauge. The usual gauge for the scalar potential is such that at infinity, this is known as the Coulomb gauge.
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Faraday's law of induction
Faraday's law can be demonstrated using a simple setup involving a permanent magnet and a coil of wire. The movement of the magnet in and out of the copper coil with multiple turns or moving the coil around the magnet changes the magnetic field through the coil. This change in the magnetic field induces an EMF in the coil. The EMF can be measured by connecting the coil to a voltmeter. The current due to the induced EMF can be measured using an ammeter or a galvanometer.
Faraday's law is a single equation describing two different phenomena: the motional EMF generated by a magnetic force on a moving wire and the transformer EMF generated by an electric force due to a changing magnetic field. The direction of the electromotive force is given by Lenz's law. The magnitude of the induced EMF depends on the magnetic field strength, the cross-sectional area of the coil, and the orientation of the coil in relation to the magnetic field.
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Voltmeters and resistors
Voltmeters are used to measure voltage, and they come in two main types: analog and digital. Analog voltmeters move a pointer across a scale in proportion to the voltage measured, while digital voltmeters give a numerical display of voltage.
The sensitivity and input resistance of a voltmeter are important factors. The sensitivity of a voltmeter refers to how much the pointer moves for a given change in voltage, and it is usually measured in ohms per volt. The input resistance of a voltmeter refers to the resistance that the voltmeter presents to the circuit it is measuring. A higher input resistance means that the voltmeter will draw less current from the circuit, which is desirable because it reduces the impact of the voltmeter on the circuit being measured.
Resistors are used in voltmeters to increase their sensitivity and input resistance. In a simple case, a resistor can be inserted in series with a moving coil galvanometer to create a voltmeter. The current required to deflect the meter pointer can be supplied by an amplifier and power supply, which increases the input resistance and reduces the current drawn from the circuit under test. This type of voltmeter is known as an amplified voltmeter.
Digital voltmeters (DVMs) measure voltage by converting the voltage to a digital value and then displaying it numerically. They are usually designed around a special type of analog-to-digital converter called an integrating converter. The accuracy of a DVM is affected by factors such as temperature, input impedance, and power supply voltage variations.
In some cases, the act of connecting a voltmeter to a circuit can affect the circuit's behaviour due to the voltmeter's own resistance. This effect is known as loading, and it can cause the meter to indicate a lower voltage than the true voltage when no meter is connected. To minimize loading, designers aim to minimize the current draw of the voltmeter movement or use an amplifier to electronically boost the current sent to the movement.
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The relationship between electricity and magnetism
Electricity and magnetism are two distinct but interconnected phenomena. Electricity is associated with stationary or moving electric charges, which can be positive or negative. When an electric charge is in motion, it creates an electric field, and this field is always present around a moving charge. On the other hand, magnetism is characterised by the existence of magnetic poles, typically referred to as "north" and "south". These poles exhibit similar behaviour to electric charges, with like poles repelling each other and opposite poles attracting.
The connection between electricity and magnetism becomes apparent when we consider the behaviour of electric charges in a magnetic field. When an electric charge moves within a magnetic field, it experiences a force that is perpendicular to the direction of its motion. This force can result in a change in potential energy, leading to the creation of an electric potential difference or voltage. This phenomenon is described by Maxwell's equations, which demonstrate that the electric and magnetic fields are perpendicular to each other in an electromagnetic wave.
Furthermore, the presence of a magnetic field can induce the movement of electric charges in a conductor. Moving a wire loop towards or away from a magnetic field will induce a current in the wire, with the direction of the current depending on the direction of movement. Additionally, an electric current flowing through a wire generates a magnetic field around it. The direction of this magnetic field can be determined using the "right-hand rule," where the direction of the magnetic field follows the fingers of your right hand when your thumb points in the direction of the current.
In summary, the relationship between electricity and magnetism is encapsulated in the concept of electromagnetism. Electric charges in motion create magnetic fields, and magnetic fields can induce the movement of electric charges. This interplay between electric and magnetic fields gives rise to various phenomena, from the behaviour of atoms to the functioning of everyday technologies such as power lines and speakers.
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Frequently asked questions
Electric potential, or voltage, is the potential difference between two points. It is the potential energy per unit charge.
Electric potential is calculated by taking an integral over the charges. The electric field is then obtained from the derivatives of the scalar potential.
In the context of electrodynamics, the scalar potential refers to electric potential, while vector potential refers to magnetic vector potential.
Magnetic potential is not commonly defined, unlike electric and gravitational potential. However, magnetic scalar potentials can be defined, but they are usually not useful.
By using standard four-vector transformation rules, if the electric and magnetic potentials are known in one inertial reference frame, they can be calculated in any other inertial reference frame.
