In the space free of current, and thus h ought to be derivable there from the gradient of a potential because we further have the potential obeys laplaces equation. Thus eqn2 yields b r a 5 where a is the vector potential. We can summarize differences between scalar and vector potentials by saying. Eece557 magnetic dipoles supplement to text fall 2008 2 1. The expression \\frac\mu i4\pi r\textbfds\, then, is the contribution \\textbfda\ to the magnetic vector potential from the circuit element \\textbfds\. It was a scalar function, related to electric eld through e rv. Scalar potential is not determined by the vector field alone. Scalar and vector magnetic potential steady magnetic field.
The electric scalar and magnetic vector potentials. The vector potential can then be written as a 1 2 b. Magnetic potential simion 2019 supplemental documentation. Both types of magnetic potential are alternate ways to reexpress the magnetic field b in a form that may be more convenient for calculation or analysis. The vector potential a is not unique only the curl of the vector potential is a well defined quantity i. Electromagnetic fields and energy mit opencourseware. The potentials vary as a function of time in accordance with the information. The electric and magnetic field vectors for a linear isotropic medium are. Of course an isolated circuit element cannot exist by itself, so, for the magnetic vector potential from a complete circuit, the line integral of this must be calculated around. The curl of a gradient is always zero so that means th.
Any function independent of position can be added to without changing. Lecture 28 antennas and radiation and the hertzian dipole. Although we cannot express the magnetic field as the gradient of a scalar potential function, we shall define a vector quantity. The magnetic field vector is the negative gradient of scalar magnetic potential, just as the electric field vector is the negative gradient of electrostatic potential. The magnetic vector potential, a, often simply called the vector potential and the magnetic scalar potential, both quantities can be used in certain circumstances to calculate the magnetic field. Vectorpotentialforthemagneticfield university of texas at.
Figure 1, which results from the maxwell equations, and in a scalar part grad div e. Dimensional analysis on the above equations shows that a has units of electric current amperes and has units of electric potential volts. Br ar 0 always the divergence of a curl of a vector field fr. Simion can solve scalar magnetic potential using the laplace equation in the same manner as electric potential is solved, and after doing so the magnetic field vector can be immediately obtained and used for particle trajectory solving. Reduced magnetic vector potential and electric scalar potential formulation for eddy current modeling abstract. Note that eqns 2 and 3 are homogeneous while eqns 1 and 4 are inhomogeneous. Us5845220a communication method and apparatus with. The knowledge of this potential and its evolution can only permit us to calculate all the force components acting upon charges. The magnetic field vector is the negative gradient of scalar magnetic. The scalar magnetic potential can be used in regions of space where there are no currents, so that nabla b 0.
Figure 2, according to which the divergence of a field pointer is a scalar. Conception of the scalarvector potential in contemporary. Pdf the special features in formation of maxwells electrodynamics and classic theory of electromagnetic field are examined. Instead of using a vector potential and a scalar potential, one can represent the electromagnetic field in terms of a pair of vector potentials, termed the hertz vectors. A scalar potential is a fundamental concept in vector analysis and physics the adjective scalar is frequently omitted if there is no danger of confusion with vector potential. A finite element formulation using the reduced magnetic vector potential and the electric scalar potential is proposed for modeling eddy current nondestructive testing problems in which the probe coil scans across the sample. Magnetic vector potential when we derived the scalar electric.
The wave equations for the electromagnetic potentials. There is, however, one important exception to this advicethe field calculation for magnetic round lenses. Magnetic potential refers to either magnetic vector potential a or magnetic scalar potential. The magnetic vector potential a and the scalar potential. Vector potential causes the wave function to change phase the schrodinger equation for a particle of mass m and charge q reads as. Now suppose the particle is bound in a strong central potential and b is relatively weak. It also points the way to a unified field theory between electricity, magnetism, and gravity. This work presents a novel contribution to the analysis of magnetic structures, making use of several interrelated concepts such as, magnetic charge density, magnetic charge, magnetic current density, magnetic current intensity, magnetic voltage, magnetic scalar potential, and electric vector potential.
A vector field ar is called the magnetic vector potential because of its analogous function to the electric scalar potential v r. Magnetic charge, magnetic current, magnetic scalar. We have to ask ourselves, which properties have this wave part. The winding order has no effect on magnetic field or vector potential but the scalar potential distribution has been reorganized because the latter highly depends on the winding order. Thus, inside the solenoid the vector potential is 2 a 1 n r i. Mathematically, this is a vector fielda smooth map from a spacetime manifold into its tangent or cotangent spaces.
Indeed, it can be seen that if and, where is an arbitrary scalar field, then the associated electric and magnetic fields are. Given maxwells four equations, demonstrate the existence of a vector magnetic potential and a scalar electric potential. Conception of the scalarvector potential in contemporary arxiv. Chapter 5 the vector potential in magnetostatics the magnetic eld is divergence free, and we have the vector identity r r f 0 for any vector function f, therefore if we write b r a, then we ensure that the magnetic eld is divergence free. However, they typically take a di erent approach to nding these. Now there is a theorem which deals with the implications of divergence of a vector. Let me start with some general properties of the vector potential. The vector a is called the magnetic vector potential. Electric and magnetic forces in lagrangian and hamiltonian. The previous prescription for expressing electric and magnetic fields in terms of the scalar and vector potentials does not uniquely define the potentials. In radiation problems, the goal is to determine the radiated elds electric and magnetic from an antennas, knowing what currents are owing on the antenna.
Magnetic vector potential, the vector whose curl is equal to the magnetic b field. Given a vector field f, the scalar potential p is defined such that. Scalar potential and conservative electric field in a. In this archival paper we present scalar potential formulations for magnetic field problems where the stationary or quasistationary current distributions are known, such as those regarding various electromagnetic devices, or magnetic systems in tokamak configurations, magnetohydrodynamic energy converters, particle accelerators, etc. Jul 08, 2018 i discussed about vector and scalars derived maxwells vector and scalar potential equations. The same derivation1 may be followed as for the electrostatic. Scalar physics concerns itself with potential and superpotential fields that do not necessarily give rise to magnetic or electric force fields, yet still have meaningful effects. The electric field can be represented by a scalar potential because in the absence of a changing magnetic field the curl of e equals zero faradays law. Pdf scalar electric and vector magnetic potentials in theory of. Request pdf magnetic charge, magnetic current, magnetic scalar potential, and electric vector potential this work presents a novel contribution to the analysis of magnetic structures, making.
The standard definition of magnetomotive force or magnetic potential involves current passing through an electrical conductor, permanent. Scalar magnetic potential is analogous to scalar potential in electric fields i. Generally, the use of vector potentials for numerical calculations should be avoided if possible, especially if the reduced scalar potential eqs. The vector potential a describes magnetic fields that possess curl wherever there is a current density j r. The term magnetic potential can be used for either of two quantities in classical electromagnetism. If divergence, of a vector field is zero everywhere, then can be expressed as the curl of a vector potential function. Reduced magnetic vector potential and electric scalar. If v is defined in terms of the line integral, the ambiguity of v reflects the freedom in the choice of the reference point r 0. This section is reserved for advanced students, with background in electricity and magnetism, and vector differential equations problem. The magnetic field is merely a spatial derivative of the vector field.
A scalar proton magnetometer is widely used for calibration, since it provides a direct measurement of the intensity of the magnetic. The scalar potential is an example of a scalar field. The vector potential, boundary conditions on a and b. Scalar potential formulations for magnetic fields produced. Information that changes as a function of time is communicated from a transmitting site to a receiving site by transmitting a signal comprising scalar and vector potentials without including ay electromagnetic field. As follows from the above consideration, it is more appropriate to write the. This is similar to how the electric field e can be conveniently reexpressed in terms of electric potential. That wont work for the magnetic field except where j 0, because the curl of b is not zero in general. We denote the two hertz vectors the electric and the magnetic ones, respectively by. Vector and scalar potentials e83 where f is an arbitrary differentiable function of x,y,z,t, then. Recall that a solenoidal field is the curl of some other vector field, e. In physics courses vector potentials come up because magnetic elds are divergence free and so have vector potentials. Scalar and vector potential physics stack exchange.
Magnetic charge, magnetic current, magnetic scalar potential. Scalar potential formulations for magnetic fields produced by. The electromagnetic field is described by two vector fields. The latter definition is more common in east european countries. A vector field ar is called the magnetic vector potential because of its analogous function to the electric scalar potential vr. They use the fact that usually a magnetic eld is the result of a stream of charged particles called a current. What is main difference between scalar and vector potential.