## Electric vs. Magnetic Forces

Electric and magnetic forces both influence the trajectory of fee particles, however in qualitatively various ways.

You are watching: Indicate which of the following will produce a magnetic field:

### Learning Objectives

Compare the impacts of the electric and also the magnetic fields on the charged particle

### Key Takeaways

Key PointsThe pressure on a charged particle as result of an electrical field is directed parallel to the electrical field vector in the situation of a confident charge, and anti-parallel in the instance of a negative charge. That does not rely on the velocity of the particle.In contrast, the magnetic force on a charge bit is orthogonal come the magnetic ar vector, and also depends on the velocity the the particle. The appropriate hand ascendancy can be supplied to recognize the direction of the force.An electric field may do work on a charged particle, if a magnetic ar does no work.The Lorentz force is the combination of the electric and also magnetic force, which space often considered together for handy applications.Electric ar lines are produced on optimistic charges and also terminate on an unfavorable ones. The ar lines of one isolated fee are directly radially outward. The electric field is tangent to these lines.Magnetic ar lines, in the instance of a magnet, are created at the north pole and also terminate top top a southern pole. Magnetic poles perform not exist in isolation. Prefer in the case of electrical field lines, the magnetic field is tangent to the ar lines. Fee particles will certainly spiral about these field lines.Key Termsorthogonal: Of 2 objects, at ideal angles; perpendicular to each other.

### Electric vs. Magnetic Forces

Force because of both electric and also magnetic pressures will affect the motion of charged particles. However, the resulting readjust to the trajectory of the particles will differ qualitatively between the two forces. Below we will easily review the two varieties of force and compare and also contrast their results on a charged particle.

### Electrostatic Force and also Magnetic pressure on a fee Particle

Recall that in a static, unchanging electric field E the pressure on a particle with fee q will certainly be:

extF= extqE

Where F is the pressure vector, q is the charge, and also E is the electric field vector. Keep in mind that the direction of F is the same to E in the situation of a positivist charge q, and also in the contrary direction in the situation of a negatively charged particle. This electrical field might be developed by a bigger charge, Q, exhilaration on the smaller charge q end a distance r so that:

extE=left | frac extF extq ight |= extk left | frac extqQ extqr^2 ight |= extkfrac extQ ight extr^2

It need to be emphasized that the electrical force F plot parallel to the electric field E. The curly of the electric force is zero, i.e.:

igtriangledown imes extE=0

A an effect of this is that the electrical field might do work and also a charge in a pure electrical field will follow the tangent the an electrical field line.

In contrast, recall that the magnetic force on a charged particle is orthogonal come the magnetic ar such that:

extF= extqv imes extB= extqvBsin heta

where B is the magnetic field vector, v is the velocity of the particle and θ is the angle in between the magnetic field and the particle velocity. The direction of F have the right to be easily determined by the usage of the ideal hand rule.

Right Hand Rule: Magnetic areas exert forces on moving charges. This force is among the most straightforward known. The direction of the magnetic pressure on a relocating charge is perpendicular come the aircraft formed by v and also B and also follows ideal hand rule–1 (RHR-1) together shown. The size of the pressure is proportional to q, v, B, and the sine that the angle in between v and also B.

If the bit velocity happens to be aligned parallel to the magnetic field, or is zero, the magnetic pressure will it is in zero. This differs from the case of an electric field, whereby the particle velocity has no bearing, on any kind of given instant, top top the magnitude or direction of the electric force.

The angle dependence of the magnetic field also causes charged particles to relocate perpendicular come the magnetic field lines in a circular or helical fashion, while a particle in an electrical field will relocate in a right line along an electrical field line.

A additional difference between magnetic and also electric pressures is the magnetic fields do no net work, since the particle motion is circular and therefore end up in the same place. We express this mathematically as:

extW=oint extB cdot extdr = 0

### Lorentz Force

The Lorentz force is the linked force ~ above a charged fragment due both electric and magnetic fields, which are often considered together for valuable applications. If a particle of fee q moves with velocity v in the visibility of an electrical field E and also a magnetic ar B, climate it will experience a force:

extF= extq< extE+ extvBsin heta>

### Electric and Magnetic ar Lines

We pointed out briefly over that the movement of charged particles family member to the ar lines differs depending upon whether one is taking care of electric or magnetic fields. There space some significant differences in between how electric and magnetic field lines are conceptualized. The electrical field lines indigenous a confident isolated fee are simply a sequence of evenly-spaced, radially command lines spicy outwards from the charge. In the instance of a negative charge, the direction the the ar is reversed. The electric field is command tangent to the field lines. Of course, we imagine the field lines are an ext densely packed the larger the fees are. One have the right to see plainly that the curl of the electrical force is zero.

Electric field Generated by allude Charges: The electrical field surrounding three different suggest charges: (a) A optimistic charge; (b) a negative charge of equal magnitude; (c) a larger an adverse charge.

If multiple charges space involved, field lines are created on optimistic charges, and also terminate on an unfavorable ones.

In the case of magnets, ar lines are created on the phibìc pole (+) and terminate on the southern pole (-) – see the listed below figure. Magnetic ‘charges’, however, always come in bag – there room no magnetic monopoles (isolated phibìc or south poles). The curl of a magnetic field generated by a traditional magnet is therefore constantly non zero. Charged particles will spiral roughly these ar lines, as lengthy as the particles have some non-zero component of velocity command perpendicular to the ar lines. Magnetic Pole Model: The magnetic pole model: two opposing poles, phibìc (+) and South (−), be separated by a distance d produce an H-field (lines).

A magnetic field may likewise be produced by a existing with the field lines envisioned together concentric circles around the current-carrying wire.The magnetic force at any point in this case can be established with the right hand rule, and will it is in perpendicular come both the current and the magnetic field.

## Constant Velocity produces a Straight-Line

If a charged particle’s velocity is parallel come the magnetic field, over there is no net force and also the particle moves in a directly line.

### Learning Objectives

Identify problems required for the particle to relocate in a right line in the magnetic field

### Key Takeaways

Key PointsNewton’s first law of movement states that if an object experiences no network force, climate its velocity is constant.A particle with constant velocity will relocate along a directly line v space.If a fee particle’s velocity is totally parallel to the magnetic field, the magnetic field will exert no pressure on the particle and thus the velocity will remain constant.In the case that the velocity vector is neither parallel no one perpendicular to the magnetic field, the component of the velocity parallel come the field will stay constant.Key Termsstraight-line motion: movement that proceeds in a solitary direction

### Constant Velocity produces Straight-Line Motion

Recall Newton’s very first law the motion. If things experiences no network force, then its velocity is constant: the thing is either at remainder (if its velocity is zero), or it move in a right line with constant speed (if its velocity is nonzero).

There are many instances where a particle might experience no net force. The particle can exist in a vacuum far away from any kind of massive body (that exert gravitational forces) and also electromagnetic fields. Or there can be 2 or more forces top top the fragment that are well balanced such the the net force is zero. This is the case for, say, a fragment suspended in an electrical field v the electrical force precisely counterbalancing gravity.

If the net force on a bit is zero, climate the acceleration is necessarily zero native Newton’s second law: F=ma. If the acceleration is zero, any kind of velocity the particle has will be kept indefinitely (or until such time as the net force is no much longer zero). Since velocity is a vector, the direction stays unchanged in addition to the speed, therefore the particle proceeds in a solitary direction, such as with a straight line.

### Charged Particles moving Parallel come Magnetic Fields

The pressure a charged fragment “feels” because of a magnetic field is dependent on the angle between the velocity vector and also the magnetic ar vector B . Recall that the magnetic force is:

Zero force When Velocity is Parallel to Magnetic Field: In the case above the magnetic pressure is zero due to the fact that the velocity is parallel come the magnetic field lines.

extF= extqvBsin heta

If the magnetic field and also the velocity room parallel (or antiparallel), climate sinθ equates to zero and also there is no force. In this instance a charged fragment can proceed with straight-line motion even in a strong magnetic field. If is between 0 and 90 degrees, then the ingredient of v parallel to B stays unchanged.

## Circular Motion

Since the magnetic pressure is constantly perpendicular to the velocity of a charged particle, the fragment will experience circular motion.

### Learning Objectives

Describe problems that lead to the circular movement of a charged particle in the magnetic field

### Key Takeaways

Key PointsThe magnetic ar does no work, so the kinetic energy and also speed that a charged fragment in a magnetic field remain constant.The magnetic force, exhilaration perpendicular to the velocity the the particle, will cause circular motion.The centripetal pressure of the bit is noted by magnetic Lorentzian force so that extqvB=frac extmv^2 extr.Solving for r above yields the gryoradius, or the radius that curvature that the path of a bit with fee q and also mass m moving in a magnetic field of strength B. The gryoradius is then offered by extr=frac extmv extqB.The cyclotron frequency (or, equivalently, gyrofrequency) is the number of cycles a fragment completes approximately its circular circuit every 2nd and is provided by extf=frac extqB2 pi extm.Key Termsgyroradius: The radius that the circular activity of a charged particle in the presence of a uniform magnetic field.cyclotron frequency: The frequency the a fee particle moving perpendicular come the direction the a uniform magnetic ar B (constant magnitude and also direction). Given by the equality the the centripetal force and also magnetic Lorentz force.

### Circular movement of a Charged bit in a Magnetic Field

Magnetic pressures can reason charged corpuscle to move in one or spiral paths. Fragment accelerators store protons adhering to circular londonchinatown.org with magnetic force. Cosmic rays will follow spiral paths once encountering the magnetic field of astrophysical objects or planets (one example being Earth’s magnetic field). The bubble chamber photo in the figure below shows charged particles moving in such bent paths. The curved londonchinatown.org of charged particles in magnetic areas are the basis of a number of phenomena and can also be offered analytically, such together in a fixed spectrometer. Mirrors the route traced by corpuscle in a bubble chamber.

Bubble Chamber: Trails of bubbles are produced by high-energy charged particles moving through the superheated fluid hydrogen in this artist’s rendition of a balloon chamber. Over there is a strong magnetic ar perpendicular come the page that causes the curved paths of the particles. The radius of the path can be offered to discover the mass, charge, and energy that the particle.

So, go the magnetic force cause circular motion? Magnetic force is always perpendicular come velocity, so the it go no work-related on the fee particle. The particle’s kinetic energy and also speed thus remain constant. The direction of movement is affected, but not the speed. This is typical of uniform circular motion. The simplest instance occurs when a charged particle moves perpendicular come a uniform B-field, together as shown in. (If this takes location in a vacuum, the magnetic field is the dominant factor identify the motion. ) Here, the magnetic force (Lorentz force) provides the centripetal force

Circular activity of Charged fragment in Magnetic Field: A negatively charged fragment moves in the aircraft of the web page in a region where the magnetic field is perpendicular right into the web page (represented through the little circles through x’s—like the tails that arrows). The magnetic force is perpendicular come the velocity, and so velocity changes in direction but not magnitude. Uniform circular activity results.

extF_ extc=frac extmv^2 extr.

Noting that

extsin heta =1

we watch that

extF= extqvB.

The Lorentz magnetic pressure supplies the centripetal force, so this terms space equal:

extqvB=frac extmv^2 extr

solving for r yields

extr=frac extmv extqB

Here, r, called the gyroradius or cyclotron radius, is the radius of curvature that the route of a charged fragment with fixed m and charge q, moving at a speed v perpendicular to a magnetic field of stamin B. In various other words, the is the radius the the circular activity of a charged particle in the visibility of a uniform magnetic field. If the velocity is not perpendicular to the magnetic field, then v is the ingredient of the velocity perpendicular to the field. The component of the velocity parallel come the ar is unaffected, since the magnetic pressure is zero for activity parallel to the field. We’ll discover the after-effects of this instance in a later on section ~ above spiral motion.

A fragment experiencing circular motion because of a uniform magnetic ar is termed to be in a cyclotron resonance. The term comes from the surname of a cyclic fragment accelerator referred to as a cyclotron, verified in. The cyclotron frequency (or, equivalently, gyrofrequency) is the variety of cycles a bit completes around its circular circuit every second and deserve to be uncovered by resolving for v above and substituting in the circulation frequency for this reason that

Cyclotron: A French cyclotron, created in Zurich, Switzerland in 1937

extf=frac extv2 pi extr

becomes

extf=frac extqB2 pi extm

The cyclotron frequency is trivially provided in radians per second by

omega=frac extqB extm.

## Helical Motion

Helical motion results when the velocity vector is no perpendicular to the magnetic field vector.

### Learning Objectives

Describe problems that result in the helical movement of a charged bit in the magnetic field

### Key Takeaways

Key PointsPreviously, we have actually seen that circular motion results when the velocity the a charged particle is perpendicular come the magnetic field. The speed and also kinetic energy of the bit remain constant, but the direction is changed at each prompt by the perpendicular magnetic force.If the velocity is no perpendicular come the magnetic field, we think about only the component of v the is perpendicular come the ar when making our calculations.The ingredient of the velocity parallel to the ar is unaffected, because the magnetic force is zero for activity parallel to the field. This to produce helical motion.Charges may spiral along field lines. If the stamin of the magnetic ar increases in the direction of motion, the ar will exert a pressure to slow-moving the charges and also even reverse their direction. This is known as a magnetic mirror.Key Termshelical motion: The movement that is created when one ingredient of the velocity is constant in magnitude and direction (i.e., straight-line motion) when the other component is continuous in speed however uniformly varies in direction (i.e., circular motion). That is the superposition the straight-line and circular motion.magnetic mirror: A magnetic ar configuration wherein the ar strength changes when relocating along a field line. The mirror result results in a tendency for charged particles to bounce ago from the high field region.

### Helical Motion

In the section on circular movement we defined the motion of a charged fragment with the magnetic ar vector aligned perpendicular come the velocity the the particle. In this case, the magnetic pressure is also perpendicular to the velocity (and the magnetic field vector, the course) at any type of given moment leading to circular motion. The speed and kinetic energy of the fragment remain constant, yet the direction is changed at each immediate by the perpendicular magnetic force. Conveniently reviews this case in the situation of a negatively charged particle in a magnetic ar directed into the page.

Circular activity of Charged fragment in Magnetic Field: A negative charged particle moves in the aircraft of the page in a an ar where the magnetic ar is perpendicular into the web page (represented by the small circles with x’s—like the tails the arrows). The magnetic pressure is perpendicular to the velocity, and so velocity transforms in direction however not magnitude. Uniform circular activity results.

What if the velocity is no perpendicular to the magnetic field? climate we take into consideration only the component of v that is perpendicular to the field when making ours calculations, so that the equations of movement become:

extF_ extc=frac extmv_perp^2 extr

extF= extqvBsin heta= extqv_perp extB

The ingredient of the velocity parallel to the field is unaffected, since the magnetic pressure is zero for motion parallel to the field. This produces helical activity (i.e., spiral motion) quite than a circular motion.

shows exactly how electrons not moving perpendicular to magnetic field lines follow the ar lines. The ingredient of velocity parallel come the currently is unaffected, and so the fees spiral along the ar lines. If field strength boosts in the direction of motion, the field will exert a pressure to slow-moving the charges (and also reverse their direction), developing a kind of magnetic mirror.

Helical Motion and Magnetic Mirrors: once a charged bit moves follow me a magnetic ar line right into a region where the ar becomes stronger, the fragment experiences a pressure that to reduce the ingredient of velocity parallel come the field. This force slows the motion along the ar line and also here reverses it, creating a “magnetic mirror. “

The activity of charged particles in magnetic areas are related to such different things together the Aurora Borealis or Aurora Australis (northern and also southern lights) and also particle accelerators. Charged particles approaching magnetic ar lines may get trapped in spiral orbits around the lines quite than cross them, as viewed above. Part cosmic rays, for example, monitor the Earth’s magnetic field lines, start the atmosphere near the magnetic poles and causing the southern or northern lights with their ionization of molecules in the atmosphere. Those corpuscle that strategy middle latitudes need to cross magnetic field lines, and many are prevented native penetrating the atmosphere. Cosmic rays space a ingredient of background radiation; consequently, they offer a higher radiation sheep at the poles 보다 at the equator.

Charged corpuscle Spiral along Earth’s Magnetic field Lines: Energetic electrons and protons, components of cosmic rays, native the Sun and also deep outer space often monitor the Earth’s magnetic field lines fairly than cross them. (Recall that the Earth’s phibìc magnetic pole is yes, really a southern pole in terms of a bar magnet. )

### Key Takeaways

Key PointsA cyclotron is a kind of bit accelerator in which fee particles accelerate outwards from the facility along a spiral path. The particles are hosted to a spiral trajectory by a revolution magnetic field and accelerated by a promptly varying electrical field.The cavity magnetron is a high-powered vacuum tube the generates microwaves utilizing the communication of a present of electrons with a magnetic field. The magnetron has applications in radar, heating, and also lighting.Mass spectrometers measure the mass-to-charge proportion of fee particles through the use of electromagnetic fields to segregate corpuscle with various masses and/or charges. It deserve to be provided to identify the elemental composition that a molecule or sample.Key Termscyclotron: very early particle accelerator in which fee particles were produced at a main source and increased spirally outward through a addressed magnetic and alternative electric fields.mass spectrometer: A maker used in massive spectrometry to find the mass composition of a offered substance.magnetron: A machine in i beg your pardon electrons are made come resonate in a specially shame chamber and thus develop microwave radiation; offered in radar, and in microwave ovens.

### Overview

Recall that the charged particles in a magnetic ar will monitor a one or spiral path depending on the alignment of your velocity vector through the magnetic ar vector. The aftermath of together motion can have profoundly helpful applications. Many technologies are based on the motion of charged particles in electromagnetic fields. Us will discover some that these, including the cyclotron and synchrotron, cavity magnetron, and mass spectrometer.

### Cyclotrons and also Synchrotrons

A cyclotron is a form of bit accelerator in which fee particles advice outwards from the center along a spiral path. The corpuscle are hosted to a spiral trajectory through a revolution magnetic field and accelerated by a quickly varying (radio frequency ) electric field. Cyclotron Sketch: map out of a particle being sped up in a cyclotron, and being ejected v a beamline.

Cyclotrons advice charged fragment beams making use of a high frequency alternate voltage which is used between 2 “D”-shaped electrodes (also dubbed “dees”). Second static magnetic field is used in perpendicular direction to the electrode plane, permitting particles to re-encounter the increasing voltage countless times at the same phase. To accomplish this, the voltage frequency must complement the particle’s cyclotron resonance frequency,

extf=frac extqB2 pi extm

with the relativistic massive m and its charge q. This frequency is given by equality that centripetal force and magnetic Lorentz force. The particles, injected close to the center of the magnetic field, boost their kinetic energy only when recirculating through the gap between the electrodes; therefore they travel outwards follow me a spiral path. Their radius will rise until the particles hit a target in ~ the perimeter the the vacuum chamber, or leaving the cyclotron using a beam tube, permitting their use. The particles accelerated by the cyclotron deserve to be supplied in bit therapy come treat some species of cancer. Additionally, cyclotrons are a good source the high-energy beams for nuclear physics experiments.

A synchrotron is an advancement upon the cyclotron in i m sorry the guiding magnetic ar (bending the particles into a close up door path) is time-dependent, being synchronized come a fragment beam of increasing kinetic energy. The synchrotron is among the very first accelerator principles that enable the building and construction of massive facilities, due to the fact that bending, beam focusing and acceleration deserve to be separated into various components.

### Cavity Magnetron

The cavity magnetron is a high-powered vacuum tube that generates microwaves making use of the communication of a stream of electrons through a magnetic field. Every cavity magnetrons covers a hot cathode v a high (continuous or pulsed) an unfavorable potential produced by a high-voltage, direct-current strength supply. The cathode is developed into the facility of an evacuated, lobed, circular chamber. A magnetic field parallel come the filament is enforced by a permanent magnet. The magnetic field reasons the electrons, attractive to the (relatively) optimistic outer part of the chamber, come spiral external in a one path, a consequence of the Lorentz force. Spaced approximately the pickled in salt of the chamber space cylindrical cavities. The caries are open along your length and also connect the usual cavity space. As electrons sweep previous these openings, they induce a resonant, high-frequency radio field in the cavity, i m sorry in turn reasons the electron to bunch into groups. Cavity Magnetron Diagram: A cross-sectional diagram of a resonant cavity magnetron. Magnetic present of pressure are parallel come the geometric axis that this structure.

The sizes of the cavities recognize the resonant frequency, and thereby the frequency the emitted microwaves. The magnetron is a self-oscillating device requiring no external aspects other 보다 a power supply. The magnetron has actually practical applications in radar, heating (as the main component of a microwave oven), and also lighting.

### Mass Spectrometry

Mass spectrometry is one analytical method that actions the mass-to-charge proportion of charged particles. That is used for determining masses the particles and determining the element composition the a sample or molecule.

Mass analyzers different the ions according to your mass-to-charge ratio. The following two legislations govern the dynamics of charged particles in electric and also magnetic areas in a vacuum:

extF= extQ( extE+ extv imes extB) (Lorentz force)

extF= extma

Equating the over expressions because that the force applied to the ion yields:

( extm/ extQ) exta= extE+ extv imes extB

This differential equation together with initial conditions totally determines the motion of a charged bit in regards to m/Q. There room many varieties of massive analyzers, utilizing either revolution or dynamic fields, and magnetic or electric fields, yet all operate according to the above differential equation.

The following figure illustrates one form of massive spectrometer. The deflections of the particles space dependent ~ above the mass-to-charge ratio. In the case of isotopic carbon dioxide, each molecule has the same charge, yet different masses. The mass spectrometer will certainly segregate the particles spatially allowing a detector to measure the mass-to-charge proportion of each particle. Since the fee is known, the pure mass can be determined trivially. The loved one abundances have the right to be inferred native counting the number of particles that each offered mass.

See more: Category:English Words That Start With The Prefix Mid ? Category:English Words Prefixed With Mid Mass Spectrometry: Schematics the a basic mass spectrometer v sector form mass analyzer. This one is because that the measurement of carbon dioxide isotope ratios (IRMS) together in the carbon-13 urea breath test.