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Dipole moment is scalar or vector

(a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole. (b) Draw the equipotential surface due to an electric dipole. Locate the points where the potential due to the dipole is zero Electric dipole moment is the product of either charges or the distance between two equal and opposite charges. It is a vector quantity.Electric dipole moment at a point on the equatorial plane: Consider a point P on broad side on the position of dipole formed of charges + q and - q at separation 2l. The distance of point P from mid-point O of electric dipole is r Electric dipole moment, p = q × d It is a vector quantity. In vector form it is written as p → = q × d →, where the direction of d → is from negative charge to positive charge. Electric Field of dipole at points on the equatorial plane The electric dipole moment is a vector quantity whose magnitude is equal to the product of charge on one dipole and distance between them. Its direction is from - q to + q. Electric dipole moment is a vector quantity The product of either charge and separation between two charges is termed as electric dipole moment. It is a vector quantity in the direction of the dipole axis from -q to +q.p→ =q(2a→) or p→ = (q) 2 a

(a) Define electric dipole moment

  1. (i) Define electric dipole moment. Is it a scalar or a vector quantity? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole. (ii) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero
  2. Brainly User Electric dipole moment is defined as the product of the magnitude of one of the charges and the distance between them. It is a a vector quantity.its direction is from the negative charge to the positive charge. It's unit is coulomb meter
  3. In the case of two separated magnetic charges, the dipole moment is trivially calculated by comparison with an electric dipole The main difference is that current density is a vector, while charge density is a scalar. 3.1 A Long, Straight Wire Now let's consider the magnetic vector potential from a long current-carrying wire, a segment.
  4. Clearly, the hydrogen atoms pushing their electrons into the more electronegative carbon only enforce the effects of each other. But, we assume for no particular reason that dipole moments must behave like vectors. We then go on to add the vectors and finally decide that the net dipole moment is 0

It is a vector quantity with magnitude equal to the product of either of the charge and the length of the electric dipole. p = q (2 a Q.3 (a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole. (b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero. OR Using Gauss' law deduce the expression for the electric field due to a uniformly charged. Since the dipole moment is useful if defined as a quantity with magnitude and direction it can be expressed in vector form by introducing d → as the displacement vector (directed from the negative charge to the positive charge). Thus in textbooks it's defined as p → = q d → Define the term electrons diople moment. Is it scalar or vector ? Watch 1 minute video. Updated On: 24-6-2020. To keep watching this video solution for FREE, Download our App. Electric dipole moment . is the product of either charge . and the distance . It is a vector quantity. Directed fro 63. Define the term electric dipole moment. Is it a scalar or a vector quantity? Answer/Explanation. Answer: Explaination: The product of the magnitude of one of the point charges constituting an electric dipole and the separation between them is termed as electric dipole moment. It is a vector quantity

It is a vector since it points in one direction (from one charge to the other), has an associated magnitude and so on. In a way, when you consider a multipole expansion it makes sense, the monopole momentum is just the net charge (a scalar), the dipole momentum a vector and from then on matrix quantities A stronger mathematical definition is to use vector algebra, since a quantity with magnitude and direction, like the dipole moment of two point charges, can be expressed in vector form where d is the displacement vector pointing from the negative charge to the positive charge

Definition. It can be defined as a vector linking the aligning torque on the object from an outside applied a magnetic field to the field vector itself. The relationship is written by. t a u = m × B. Where τ is the torque acting on the dipole, B is the outside magnetic field, and m is the magnetic moment Is it a scalar or a vector? Define magnetic dipole moment. What are its units? Is it a scalar or a vector? Books. Physics. NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless. Chemistry. NCERT P Bahadur IIT-JEE Previous Year Narendra Awasthi MS Chauhan. Biology. NCERT NCERT Exemplar NCERT Fingertips. Magnetic moment, also known as magnetic dipole moment, is the measure of the object's tendency to align with a magnetic field. Magnetic Moment is defined as magnetic strength and orientation of a magnet or other object that produces a magnetic field. The magnetic moment is a vector quantity Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole. (All India 2013) Answer: Electric dipole moment: It is the product of the magnitude of either charge and distance between them

A convenient measure of polarization is P= dipole moment per unit volume. Note that P is vector.P is known as polarization vector. If polarization is uniform then there will not be any net local charge inside the substance This product is called the magnetic dipole moment (or, often, just magnetic moment) of the loop. We represent it by $\mu$: \begin{equation} \label{Eq:II:14:32} \mu=Iab. \end{equation} The vector potential of a small plane loop of any shape (circle, triangle, etc.) is also given by Eq The vector \[ \mathbf {p} =\int _{V'}\rho (\mathbf {r} ')\mathbf {r} 'dV' \] is called the electric dipole. And its magnitude is called the dipole moment of the charge distribution. This terms indicates the linear charge distribution geometry of a dipole electrical potential

Ans. (i) In stable equilibrium the dipole moment is parallel to the direction of the electric field (i.e., θ = 0). (ii) In unstable equilibrium PE is maximum, so θ = π, i.e; the dipole moment is antiparallel to the electric field. Q 5. Define electric field strength. Is it a vector or a scalar quantity? Ans The dipole moment is the product of charge and the distance between them. It is a vector quantity. Therefore option 4 is correct. The rate of flow of charge is called electric current. It is a scalar quantity. Power (P): It is defined as the rate at which work is done. It is a scalar quantity Bond dipole moment is the dipole moment between the single bond of a diatomic molecule, while the total dipole moment in a polyatomic molecule is the vector sum of all the bond dipoles. Thus, total molecular dipole moment depends on the factors like- differences in the sizes of the two atoms, hybridization of the orbitals, direction of lone. The magnetic moment may be considered, therefore, to be a vector. The direction of the magnetic moment points from the south to north pole of the magnet (inside the magnet). The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment is diploe moment vector or a scalar quantity - Physics - TopperLearning.com | 474

Define Electric Dipole Moment

Define electric dipole moment. Is it a scalar or vector? Give its SI unit. Ans. Its magnitude is given by the product of magnitude of either charge and distance between them. It is represented by 'p'. p = q (2a). It is a vector quantity and its SI unit is Cm. q A B V osbincbse.com OSBINCBSE.COM OSBINCBSE.CO Q.27 Define dipole moment of an electric dipole. Is it a scalar or a vector? (1) Q.28 State Gauss's law in electrostatics. A cube with each side a is kept in an electric field given by ' ,⃗ = C T ̂, (as is shown in the figure), where C is a positive dimensional constant. Find out (3) (i) the electric flux through the cube, an between the heart dipole moment and the potential it produces at any point in or on the boundary of the medium. Let the heart dipole be represented by a vector* P = ipz + Vv j + k p2 where pz, p anc ' Pz a'e the three scalar com-ponents of the dipole moment and are func-tions of time, and i, j and k are standard uni Vector potential of a magnetic dipole produced by a current loop By analogy with the electrostatic case, we deduced that when the magnetic dipole is m~= m~z B~ dipole= 0 4ˇr3 [2mcos ^r+ msin ^] (11) We want to nd a vector potential so that B~ dipole= r^~ A~. The curl in spherical polars is, r^~ A~= 1 rsin [@ @ (sin A ˚) @A @ ]^r+ 1 r [1 sin.

Define the term 'electric dipole moment

  1. 5.Define dipole moment of an electric dipole. Is it a scalar quantity or a vector quantity? [Foreign 2012; All India 2011] Ans.Electric dipole moment of an electric dipole is equal to the product of its charges and the length of the electric dipole.It is denoted by p. Its unit is coulomb-metre
  2. (2) diamagnetism: the orbital speed of the electrons is altered in such a way as to change the orbital dipole moment in a direction opposite to the field. Whatever the cause, we describe the state of magnetic polarization by the vector quantity M = magnetic dipole moment per unit volume
  3. The electric dipole moment for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance between them and the defined direction is toward the positive charge. The electric field of an electric dipole can be constructed as a vector sum of the point charge fields of the two charges: Direction of.
  4. 8.3 The Scalar Magnetic Potential. The vector potential A describes magnetic fields that possess curl wherever there is a current density J (r).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 Laplace's equation
  5. (time-averaged) power in electric dipole radiation is P E1 = 2a2e2ω4 3c3. (25) This charge distributionalso has a magnetic dipole moment and an electricquadrupole moment (plus higher moments as well!). Calculate the total radiation fields due to the E1, M1 and E2 moments, as well as the angular distribution of the radiated power an
  6. field is its dipole moment. This is a vector quantity, and the torque is a maximum when the dipole moment is at right angles to the electric field. At a general angle, the torque τττ, the dipole moment p and the electric field E are related by τ= p ×××× E. 3.1.1 The SI units of dipole moment can be expressed as N m (V/m) −1. However.
  7. Dipole moments are a vector quantity. The magnitude is equal to the charge multiplied by the distance between the charges and the direction is from negative charge to positive charge: μ = q · r. where μ is the dipole moment, q is the magnitude of the separated charge, and r is the distance between the charges

There are two sources of magnetic dipoles: currents and intrinsics magnet moments of elementary particles. In either case, we have a magnetic dipole moment m~that gives the magnitude and direction of the magnetic dipole. This magnetic dipole moment is directly analagous to the electric dipole moment p~, so we can write, B~= 0 4ˇ 3(m~^r)^r m~ r The multipole expansion is expressed as a sum of terms with progressively finer angular features. For example, the initial term—called the zeroth, or monopole, moment—is a constant, independent of angle. The following term—the first, or dipole, moment—varies once from positive to negative around the sphere where is the dipole moment of a dipole kept in a uniform electric field . Cross Product or Vector Product The vector product or cross product of two vectors is defined as a vector having magnitude equal to the product of the magnitudes of two vectors with the sine of angle between them, and direction perpendicular to the plane containing the.

Ask Questions, Get Answers Menu X. home ask tuition questions practice papers mobile tutors pricin Electric dipole moment, It is a vector quantity. In vector form, it is written as , where the direction of is from negative charge to positive charge. Electric field of dipole at points on the equatorial plane : The magnitudes of the electric field due to the two charges and are given by, The direction of and are shown in the figure. The. A dipole moment is a measurement of the separation of two opposite electrical charges. Dipole moments are a vector quantity. The magnitude is equal to the charge multiplied by the distance between the charges and the direction is from negative charge to positive charge: μ = q · r. where μ is the dipole moment, q is the magnitude of the. The Helbig method (Schmidt and Clark, 1997, 1998; Phillips, 2005) is based on the observation (Helbig, 1963) that the vector components (mx, my, mz) of the total magnetization of a compact source can be estimated from the first moments of the vector components (Bx, By, Bz) of the anomalous magnetic field produced by the source.Here we use the convention of geomagnetism that the x-axis points. The integrated induced dipole moment , for vector interference, or the scalar modulation , for scalar interference, was assumed to be a function of the impulse (integrated force) , or its magnitude , experienced by the molecule in a collision

Define the term electric dipole moment

  1. Electric lines flux can be defined as the scalar product of electric flux intensity and vector area. The dipole moment of an electric dipole is defined as the product of the two equal charges and perpendicular distance between them i.e. dipole moment. It includes every relationship which established among the people
  2. g articles, quizzes and practice/competitive program
  3. Vector Learning Oggmented with Charges on Individual Realistic Atomic Positions to Optimize Regression. This is the code used to produce the results in: Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles (M. Veit, D. M. Wilkins, Y. Yang, R. A. DiStasio Jr., M. Ceriotti, arXiv:2003.12437 (2020))
  4. ation of the spacecraft equivalent magnetic dipole moment vector m SC provided that its position inside the spacecraft is known (Ness et al 1971). Deter

(i) Define electric dipole moment

define electric dipole moment

physical chemistry - Is dipole moment a vector

  1. g the bond angles are 120° apart
  2. exchange of scalar or pseudoscalar or vector gauge bosons are enumerated in Ref. [10]. Another theoretical frame- on limits from the neutron electric dipole moment experi-ments; however, it may be much smaller, relaxing the The dipole-dipole potential associated with exchang
  3. We transform the 4-vector potential from K' to K and check if it transforms into a vector potential due to a magnetic dipole m and a scalar potential due to an electric dipole p to first order. Details of the calculation: In the rest frame K' of the magnetic dipole we have A' μ = (0,A' x,A' y,A' z). The dipole is at rest at the origin in K'
Important questions class 12 physics electric charges andCoulomb's law - Wikipedia

Define Dipole Moment of an Electric Dipole

{However, magnetic vector potential is not directly associated with work the way that scalar potential (e.g. Electric potential V) is associated with work} Work done against the electric field E is stored as electric potential energy U given in terms of electric dipole moment p and E as B) Magnetic Vector Potential 12 Abstract. We propose a new concept for determining the interior magnetic field vector components in neutron electric dipole moment experiments. If a closed three-dimensional boundary surface surrounding the fiducial volume of an experiment can be defined such that its interior encloses no currents or sources of magnetization, each of the interior vector field components and the magnetic scalar. Consider a short magnetic dipole NS. Let M be the magnetic moment of the dipole. Since the magnetic potential is a scalar quantity, the resultant potential at a point P is given by. Case 1: If P is a point on the axis of the dipole, then θ = 0° or θ = 180° and Cos θ = ± 1 2. An arbitrary surface enclosed a dipole. What is the net electric flux through the surface? [Ans : zero] 3. (a) An electrostatic field line is a continuous curve. That is field lines cannot have sudden breaks. Why is it so? (b) Define electric dipole moment. Is it a scalar or a vector quantity? What is its SI unit (vector bor scalar a) or magnetic dipole moment M 1. • We are currently working towards a new, precision measurement of E PNC /bon the → transition of atomic cesium in our laboratory. • There are currently two precise determinations of the vector polarizability b. • One uses a theoretical value of the hyperfine-changing magnetic dipole.

Q3 a Define electric dipole moment Is it a scalar or a

  1. The position vector of the center of mass of the system is then given by r 1 M from MATH 229 at College of Charlesto
  2. The following figure shows the power pattern in dipole approximation. It can be seen that the two lobes are symmetric about the dipole. The distance from the dipole to t he lobe at any point gives the relative power in that direction with respect to the maximum. The total radiated power varies as the fourth power of the frequency
  3. @article{osti_21210273, title = {Magnetic dipole moment of vector mesons}, author = {Castro, G Lopez and Sanchez, G Toledo}, abstractNote = {We analyze the sensitivity to the vector-meson magnetic dipole moment of radiative processes involving the production and decay of vector mesons. These studies assume that vector mesons are stable particles
  4. We analyze the quantum phase effects for point-like charges and electric (magnetic) dipoles under a natural assumption that the observed phase for a dipole represents the sum of corresponding.
  5. We address a long-standing debate over whether classical magnetic forces can do work, ultimately answering the question in the affirmative. In detail, we couple a classical particle with intrinsic spin and elementary dipole moments to the electromagnetic field, derive the appropriate generalization of the Lorentz force law, show that the particle's dipole moments must be collinear with its.

Jul 06, 2021 - Radiation Notes | EduRev is made by best teachers of Electrical Engineering (EE). This document is highly rated by Electrical Engineering (EE) students and has been viewed 100 times a unit radial vector and a unit vector in the direction of the magnetic field is the cosine of the desired angle.) 6. Show that for a dipole field line with equatorial crossing distance L, the radius of curvature* of at the equator is L/3. (Note that this is 1/3 the radius of curvature of a geocentric circle of radius L)

electrostatics - If dipole moment is a vector $q×d$, then

the magnetic vector potential and electric scalar potential, respectively. Because in (3) the magnetic field has no divergence. the identity in (6) allows us to again define the vector potential A This forms an electric dipole with moment . p=qdl i. (3) If we can find the potentials and fields from this simpl 6.2 Scalar and Vector Potentials The E and B fields define a total of six functions in space and time. It turns out that these fields are not independent and that one needs fewer functions to uniquely determine the electromagnetic field. The vector potential A and the scalar po- The dipole moment p is defined as p(t) = q(t)ds. (6.16 the dipole moment, p~ in terms of spherical coordinates then we can always put it in a form that has no φ dependence. Writing this vector in a general sense it would look like the following. p~ = (p~· ˆr)ˆr +(p~·θˆ)θˆ Since the above way or writing the dipole moment is entirely general it must be an equiva

Define the term electrons diople moment

The monopole moment (Q) is a scalar, the dipole moment (p) is a vector, the quadrupole moment (Qij) is a second-rank tensor, and so on (a) Find all nine components of Qij for the given configuration (assume the square has side a and lies in xy-plane, centered at origin) (b) How would define the octopole moment? Express the octopole term in. is a unit vector along r, r is the distance between the magnetic field source and the measurement point, and → m is called the magnetic dipole moment. The derivation of this equation can be found in many textbooks on elect romagnetics . This is a very convenient equation for estimating the field p roduced by many magnetized objects Problem 1. A time dependent dipole Consider an electric dipole at the spatial origin (x = 0) with a time dependent electric dipole moment oriented along the z-axis, i:e: p(t) = p o cos(!t)z^ ; (1) where z^ is a unit vector in the z direction. (a)Recall that the near and far elds of the time dependent dipole are qualitatively dif-ferent For example, the interaction energy (a scalar = rank-0 tensor) between a magnetic field B of magnitude B (i.e. B is the length of the vector B) and a magnetic dipole moment m with magnitude m is given by the dot-product of the two vectors: The equations assume a Cartesian coordinate system with unit vectors e x, e y, e z of length 1 Parity. The integral for the dipole moment is essentially a sum of an infinite number of vectors - each vector in the sum is the position vector multiplied by a scalar function of the position (the probability density)

Physics MCQs for Class 12 with Answers Chapter 1 Electric

Electric dipole moment, It is a vector quantity. In vector form, it is written as , where the direction of is from negative charge to positive charge. Electric field of dipole at points on the equatorial plane : The magnitudes of the electric field due to the two charges and are given by, The direction of and are shown in the figure. The. Start studying Physics and Math Review Ch.5 (Electrostatics and Magnetism). Learn vocabulary, terms, and more with flashcards, games, and other study tools As with scalar and vector operators, a definition equivalent to Eq. (24) may be given that involves the commutation relations of Tij with the components of angular momentum. As an example of a tensor operator, let V and W be vector operators, and write Tij = ViWj. (25) Another example of a tensor operator is the quadrupole moment operator. Radiation from electric dipole moment Masatsugu Sei Suzuki and Itsuko S. Suzuki involves the use of the Lienard-Wiechert scalar and vector potential, and is fairly elaborate. where is the angle between the acceleration vector and the line from the charge to the observer

Transcribed image text: 0.3: )Consider a volume contains monopoles, dipoles, quadrupoles and octopoles. Expand the electric potential by multipole expansion, and write potential terms for each of above. (The monopole moment ) is a scalar, the dipole moment (p) is a vector, the quadrupole moment (Q) is a second-rank tensor, and so on (a) Find all nine components of Q, for the given. where p is the dipole moment, and the symbol × refers to the vector cross product. The field vector and the dipole vector define a plane, and the torque is directed normal to that plane with the direction given by the right-hand rule

Magnetic Torque and Magnetic Dipole Moment - YouTube

electromagnetism - Why is electric dipole moment a vector

The size (length) of the dipole is the distance between the point charges times the magnitude of the charges. Often, especially in chemistry, this size (a scalar) is also referred to as dipole moment. In chemistry sizes of molecular dipole moments are often quoted to indicate the amount of charge separation in a molecule. Usually chemists are. → Electric dipole moment is a vector quantity acting from - q to + q charge. → In a uniform electric field, the net force on the dipole is zero and it experiences a torque only, → In a uniform electric field, a dipole has only rotatory motion Elements of Vectors 24 18. Collinear vectors : Two or more vectors parallel or antiparallel to each other are called collinear vectors. 19. Coplanar vectors : Vectors lying on the same plane are called coplanar vectors and the plane in which they lie is called the plane of the vectors. 20. Unit vector : It is a vector whose magnitude is unity. A unit vector parallel to a given vector We now define the dipole moment ~p by the formula ~p = X i ~riqi (8) (e.g., Jackson 1975, p. 137), where we note the dipole moment is a vector, has dimensions of length times charge, and in MKS units has units of mC. (The dipole moment is a vector, as just noted, and so is a rank 1 tensor.) The traditional symbol for the dipole moment p The magnetic dipole moment ( µ) is a vector defined as µ = i A whose direction is perpendicular to A and determined by the right-hand rule. Like a compass needle, the magnetic moment ( µ) will seek to align with an externally applied magnetic field ( B o ). It will experience a torque ( τ) or twisting force given by the vector cross product.

11/4/2004 The Polarization Vector.doc 2/3 Jim Stiles The Univ. of Kansas Dept. of EECS We will therefore define an average dipole moment, per unit volume, called the Polarization Vector P(r). () 2 dipole moment r unit volume n C vm ⎡ ⎤ ⎢ = ⎥ ∆ ⎣ ⎦ ∑p P where p nis one of N dipole moments in volume ∆v, centered at position r 4. Oscillating Electric Dipole Consider an oscillating electric dipole where the two charges are separated by a short distance s and the charges oscillate back and forth as Q(t)=Q 0ei! t. (a) What is the current I(t)? (b) What is the dipole moment p(t)? (c) What is the vector potential in terms of the retarded dipole moment p r

Electric dipole moment - Wikipedi

where M is the magnetic moment of the dipole, r is the radial distance of the point of observation from it, and 0 is the angle between the position vector of the point and the reversed vector moment of the dipole. If the di­ pole is axial, centered, and southward-directed, 6 is the colatitude. From this equation it is readily possible t where m is the magnetic dipole moment: mrjrV 1 2 d. 7 V =¢ ¢¢ò () ¢ Taking the curl of A d, applying the product rule and keeping in mind that m is a fixed vector, for the magnetic field produced by a point dipole one gets: B mrr mr 4 r 3 d .8 0 2 5 () m p = ⋅-According to the Curie symmetry principle [5], the effects generated by a. Figure 9-1 A point dipole antenna is composed of a very short uniformly distributed . current-carrying wire. Because the current is discontinuous at the ends, equal magni­ tude but opposite polarity charges accumulate there forming an electric dipole. By symmetry, the vector potential cannot depend on the angle . 4, A. = Re [A. (r, 0) ei

Magnetic Dipole Moment - Definition and Formula Magnetic

The angle between vectors is used when finding the scalar product and vector product. The scalar product is also called the dot product or the inner product. It's found by finding the component of one vector in the same direction as the other and then multiplying it by the magnitude of the other vector Overview¶. Magnetic potential refers to either magnetic vector potential (A) or magnetic scalar potential ().Both types of magnetic potential are alternate ways to re-express the magnetic field (B) in a form that may be more convenient for calculation or analysis.This is similar to how the electric field (E) can be conveniently re-expressed in terms of electric potential () Physikalisch-chemisches Praktikum I Dipole Moment { 2016 induced dipole moment ~I is always oriented in the direction of E~0, i.e. that is a scalar. If the molecules have a permanent dipole moment ~ 0, the total dipole moment in and external eld is: ~= ~ 0 + ~I (14) Orientation polarization P is only observed when the molecules have a permanen Coordinate Systems Up: Scalar and Vector Calculus Previous: Vector Integration by Parts Contents Integration By Parts in Electrodynamics. There is one essential theorem of vector calculus that is essential to the development of multipoles - computing the dipole moment Moment is a concept that gives a measure of the effect of a physical property around an axis. It also gives a measure of the distribution. • Momentum is a vector while moments can be either vector or scalar. • Momentum is a conserved property in the universe, and independent of the frame of reference

Define magnetic dipole moment

11/21/2004 The Magnetic Dipole 1/8 Jim Stiles The Univ. of Kansas Dept. of EECS The Magnetic Dipole Consider a very small, circular current loop of radius a, carrying current I. Since the contour C is a circle around the z -axis, with radius a, we use the differential line vector: ()cos sin x dipole moments is optically allowed, creating bright modes, whereas the out-of-phase coupling is dark due to the cancellation of the oppositely oriented dipole moments (in the quasistatic approximation). These bright modes are electric dipolar in nature and readily couple to scalar (i.e., linearly or circularly polarized) beams of light Summary. In many physical applications, and in particular in geomagnetism, the harmonic expansion (or integral expression) of the scalar and vector potentials at an arbitrary point P of a magnetic dipole of moment M situated at P 0 relative to a specified origin O is required. In the present paper, the above expansions and integrals in three‐dimensional Cartesian, spherical, cylindrical and.

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