Click here to go to the applet.
This applet is a magnetostatics
demonstration which displays the
magnetic field in a number of situations.
You can select from a number of fields and see how
particles move in the field if it is treated as either a velocity field
(where the particles move along the field lines) or an actual force
field (where the particles move as if they were little magnets).
This helps you visualize the field. You can also view the vector potential
(A).
When you start the applet, you will see 500 particles moving in the
field of a current line. By default the
particles are treating the field as a velocity field, which means
that the magnetic field vectors determine how fast the particles are
moving and in
what direction. In this case, the particles follow the field lines
around the current line. Of course in real life, particles do not
follow the field lines; magnetized particles will align themselves with
the field lines and then move closer to the source of the field,
whereas moving charged particles are accelerated in a direction
perpendicular to the field (and their velocity).
The Field Selection popup will allow you to select a
vector field. The choices are:
- current line: This is the field of an infinitely long
line of current.
- current line double: This is two lines of current
moving in the same direction.
- cur line double + ext: This is two lines of current
moving in the same direction, plus a uniform external field.
- current line dipole: This is two lines of current
moving in opposite directions.
- cur line dipole + ext: This is two lines of current
moving in opposite directions, plus a uniform external field.
(In fluid dynamics this field is called the
Lamb
dipole.)
- uniform field:
A uniform magnetic field; the direction is adjustable by modifying
the two angles theta and phi.
- moving charge:
The field of a moving point charge.
- fast charge:
The field of a point charge moving close to the speed of light.
The ratio between the speed of the particle and the speed of light
is adjustable.
- moving charge double:
The field of two moving point charges.
- moving charge dipole:
The field of two point charges moving in opposite directions.
- current loop:
Current moving in a circular loop. This field is equivalent to that
of a flat disc magnet; the north pole is at the top
by default.
- loop pair:
Current moving in two circular loops (or two flat disc magnets).
The size of the loops and the separation are both adjustable.
Also you can introduce a vertical offset between the two loops.
- loop pair opposing:
Two circular loops with current moving in
opposite directions. (Or two opposing flat disc magnets.)
- loop pair stacked:
Current moving in two stacked circular loops. (Or two stacked disc
magnets.)
- loop pair stacked, opp.:
Two stacked circular loops with current moving in
opposite directions. (Or two stacked disc
magnets with their north poles pushed together.)
- concentric loops:
Two concentric circular loops with the current moving in
opposite directions. The field is the same as that of a flat
ring magnet.
- solenoid:
A coil of wire with current running through it. (In real life the coil
would need to be attached to something in order to have current running
through it, of course.)
The diameter of the coil, the height, and the number of turns are
adjustable. The field is the same as that of a magnetic rod
(assuming a large number of turns).
- toroidal solenoid:
A coil of wire wrapped around a torus (donut). Outside the torus,
the field is fairly weak.
- horseshoe electromagnet:
A coil of wire wrapped around half a torus.
- square loop:
Current moving in a square.
- corner:
Current rounding a corner.
- magnetic sphere:
The field of a magnetized sphere, with the north pole at the top.
This is similar to the earth's magnetic field, except upside down,
because the earth's north pole (even the "magnetic north" as opposed
to the geographic north)
is actually its magnetic south pole.
See this page
and this page.
- monopole attempt:
This is a simulation of what would happen if you tried to make a
magnetic monopole (a magnet with only a north pole and no south pole)
by taking a bunch of square magnets and forcing them into a cube with
their south poles in the center. Instead of getting a monopole,
you would find that the gaps between the magnets would act as south poles,
and the field there would be much stronger than on the faces of the
magnets. If you could force them together perfectly with no gaps,
there would be no field at all anywhere because all the currents would
cancel out. (This field is so slow to compute that we display field vectors
by default instead of particles.)
The Display popup will allow you to select how the field
is displayed:
- Display: Particles (Vel.) means particles will move through
the field, with the magnetic field vectors (B) determining their velocity.
Note that the particles are only a educational device
intended to show what the field looks like;
in real life, particles would not move in this manner.
- Display: Particles (A Field, Vel.) means particles will move,
with the vector
potential (A) determining their velocity.
- Display: Field Vectors shows you the field vectors at an array
of locations.
- Display: Field Vectors (A) shows you the vector potential
at an array of locations.
- Display: Field Lines shows you the field lines. The
Line Density slider controls how many lines to draw. The
color indicates the field strength.
- Display: Parts (Magnetic) means that magnetized particles
(little current loops) will move through the field in a realistic fashion.
Particles are displayed as little arrows; their north
pole is at the head of the arrow and the south pole is at the tail. (So,
the arrow represents the magnetic moment vector.) They align
themselves with the field lines and then move closer to the
source of the field. In the case of a uniform field; they don't move;
they just align themselves with it.
A fair amount of damping is used so that the particles don't
oscillate very much if they are out of alignment with the field.
- Display: Mag View Film simulates
the behavior of
magnetic
viewing film. This requires slicing to be on.
The Mouse popup controls what happens when you click on the box.
If you set it to Adjust Angle or Adjust Zoom, you can
adjust the orientation or size of the 3-d view by clicking and
dragging on the box.
The Slice popup allows you to look at planar slices of the box
rather than looking at the contents of the entire box.
If the popup is set to No Slicing, you view the entire
box. Otherwise you will see the box sliced in one of three
directions. The location of the slice can be adjusted by dragging
the line running along the sides of box near the slice.
The Stopped checkbox will stop the particles.
The Reverse checkbox will reverse the direction of all the
field vectors.
The Reset button can be used to reset the positions of
all the particles to random values.
The Field Strength slider makes the field stronger or weaker,
and also adjusts the brightness of the field vectors if you
have Display: Field Vectors selected.
The Vector Density slider controls the number of vectors present
if you have Display: Field Vectors selected.
It controls the resolution of the viewing paper if you have
Display: Mag View Film selected.
The Number of Particles slider allows you to reduce the number
of particles, which can be useful if you want to watch the behavior of
just a few of them. Also it might speed things up if you have fewer
particles.
A few additional field-specific sliders may be present,
depending on the field you have selected.
Click here to go to the applet.
java@falstad.com
A far higher place must be assigned to Judaism among the competitors for the allegiance of Europe. The cosmopolitan importance at one time assumed by this religion has been considerably obscured, owing to the subsequent devolution of its part to Christianity. It is, however, by no means impossible that, but for the diversion created by the Gospel, and the disastrous consequences of their revolt against Rome, the Jews might have won the world to a purified form of their own monotheism. A few significant circumstances are recorded showing how much influence they had acquired, even in Rome, before the first preaching of Christianity. The first of these is to be found in Cicero’s defence of Flaccus. The latter was accused of appropriating part of the annual contributions sent to the temple at Jerusalem; and, in dealing with this charge, Cicero speaks of the Jews, who were naturally prejudiced against his client, as a powerful faction the hostility of which he is anxious not to provoke.330 Some twenty years later, a great advance has been made. Not only must the material interests of the Jews be respected, but a certain conformity to their religious prescriptions is considered a mark of good breeding, In one of his most amusing satires, Horace tells us how, being anxious to shake off a bore, he appeals for help to his friend Aristius Fuscus, and reminds him of217 some private business which they had to discuss together. Fuscus sees his object, and being mischievously determined to defeat it, answers: ‘Yes, I remember perfectly, but we must wait for some better opportunity; this is the thirtieth Sabbath, do you wish to insult the circumcised Jews?’ ‘I have no scruples on that point,‘ replies the impatient poet. ‘But I have,’ rejoins Fuscus,—‘a little weak-minded, one of the many, you know—excuse me, another time.‘331 Nor were the Jews content with the countenance thus freely accorded them. The same poet elsewhere intimates that whenever they found themselves in a majority, they took advantage of their superior strength to make proselytes by force.’332 And they pursued the good work to such purpose that a couple of generations later we find Seneca bitterly complaining that the vanquished had given laws to the victors, and that the customs of this abominable race were established over the whole earth.333 Evidence to the same effect is given by Philo Judaeus and Josephus, who inform us that the Jewish laws and customs were admired, imitated, and obeyed over the whole earth.334 Such assertions might be suspected of exaggeration, were they not, to a certain extent, confirmed by the references already quoted, to which others of the same kind may be added from later writers showing that it was a common practice among the Romans to abstain from work on the Sabbath, and even to celebrate it by praying, fasting, and lighting lamps, to visit the synagogues, to study the law of Moses, and to pay the yearly contribution of two drachmas to the temple at Jerusalem.335 Jeff’s hand was quietly coming down. “What happened to you?” begged Sandy. “Something new has come up, sir. I was waiting there by my ship a good while back, and I heard another one cruising and spiraling, shooting the field, I guess, because he came in and set down. My crate, just the way you ordered, was down by the grove, not in plain sight in the middle of the course. But Jeff set his ship down, left the engine running, and went off. I stayed hid to see what would happen, but when he didn’t come back, I thought I’d better go and find you—and see if it meant anything to you.” She stood alone, with the sticky, wet knife in her hand, catching her breath, coming out of the madness. Then she stooped, and pushing the branches aside felt about for her pistol. It lay at the root of a tree, and[Pg 80] when she had picked it up and put it back in the holster, there occurred to her for the first time the thought that the shot in the dead stillness must have roused the camp. And now she was sincerely frightened. If she were found here, it would be more than disagreeable for Landor. They must not find her. She started at a swift, long-limbed run, making a wide detour, to avoid the sentries, bending low, and flying silently among the bushes and across the shadowy sands. The year 1756 opened with menaces to England of the most serious nature. The imbecility of the Ministry was beginning to tell in the neglect of its colonies and its defences. France threatened to invade us, and a navy of fifty thousand men was suddenly voted, and an army of thirty-four thousand two hundred and sixty-three of native troops; but as these were not ready, it was agreed to bring over eight thousand Hessians and Hanoverians. To pay for all this it was necessary to grant excessive supplies, and lay on new duties and taxes. In presenting the money bills in the month of May, Speaker Onslow could not avoid remarking that there were two circumstances which tended to create alarm—foreign subsidies and foreign troops introduced, and nothing but their confidence in his Majesty could allay their fears, or give them confidence that their burdens would be soon reduced. There was, in fact, no chance for any such reduction, for wars, troubles, and disgraces were gathering around from various quarters. The first reverse came from the Mediterranean. MUCH to their amazement, the boys waked up the next morning in Nashville, and found that they had passed through the "dark and bloody ground" of Kentucky absolutely without adventure. After drawing and dividing the rations and cartridges. Si gave the boys the necessary instruction about having their things ready so that they could get them in the dark the next morning, and ordered them to disregard the bonfires and mirth-making, and lie down to get all the sleep they could, in preparation for the hard work of the next day. Then, like the rest of the experienced men, who saw that the campaign was at length really on, and this would be the last opportunity for an indefinite while to write, he sat down to write short letters to his mother and to Annabel. "Bully for the Wild Wanderers of the Wabash," Shorty joined in. "They're the boss regiment in the army o' the Cumberland, and the Army o' the Cumberland's the boss army on earth. Hooray for US Co. Le's have a speech. Where's Monty Scruggs?" "Bring a light, do—I can't abide this dark." Albert suddenly began to look uneasy. After all he was not really drunk, only a little fuddled. He walked straight, and his roll was natural to him, while though he was exceedingly cheerful, and often burst into song, his words were not jumbled, and he generally seemed to have a fair idea of what he was saying. "But I heard what the doctor said to you." "A purty accident—wud them stacks no more dry than a ditch. 'Twas a clear case of 'bustion—fireman said so to me; as wicked and tedious a bit o' wark as ever I met in my life." Calverley stept from the shadow of the cliff, and beheld a meteor in the sky, brightening and expanding, as the clouds opened, until it assumed the appearance of a brilliant star, of astonishing magnitude, encircled by dazzling rays, which, in a singular manner, were all inclined in one direction, and pointing to that part of the horizon where lay the rival of England—France. The foreman's face assumed a deeper hue than usual: he looked fiercely at the galleyman, but there was a determination in the weather-beaten face that made him pause ere he spoke. "Galleyman," he at length said, "you knew the business before you came: if you be so fond of saving old witches' lives, why didn't you say so, that I might not now be in this dilemma?" "No, no, not the boy," replied Merritt, rather impatiently.