Click here to go to the applet.
This applet demonstrates electrostatics in two dimensions.
There is also a three dimensional applet
which is more accurate but less flexible.
When the applet starts up you will see the electric field of two
positive charges. The yellow circle represents the charge;
the white circles around it are equipotential lines (lines of constant
potential). The field lines are also drawn in white. The green arrows
indicate the electric field. The charge
can be dragged around the screen with the mouse.
In general, yellow represents positive charge, and blue represents
negative charge.
Conductors, dielectrics, and media with bound charges will show up as
gray. Click on the objects, or the outer edge of the objects,
to see what type they are.
Since this is a 2-D simulation, the electric field of charges is
proportional to 1/r, like a line charge, not 1/r2 like a point charge. It should be
treated as a 2-D cross section, where all the charges and conductors extend in and
out of the screen.
The Example popup can be used to view some interesting
pre-defined experiments. Once an experiment is selected,
you may modify it all you want. The choices are:
- Double Charge: Two positive charges.
- Single Charge: A single positive charge.
- Dipole Charge: One positive and one negative charge.
- Charge + Plane: A charge near a grounded
conductor. Note that the field in the upper half is nearly
the same as in Dipole Charge (it should be exactly the same). The
blue color on the conductor indicates negative surface charge, which is
put there to balance the external field and
maintain the conductor at ground.
- Dipole + Uniform: A dipole in a uniform field.
- Quadrupole Charge: Two positive and two negative
charges.
- Conducting Planes: Two conductors fixed
at opposite potentials. The yellow and blue color on the outer edge of
the conductors indicate positive and negative surface charges. Charge
is added to or removed from each conductor as needed to maintain the
potential.
- Charged Planes: Two uniformly charged planes.
- Conducting Cylinder: A cross section of a conducting
cylinder at positive potential.
- Grounded Cyl + Charge: A cross section of a grounded
conducting cylinder with a charge next to it.
- Grounded Cyl + Field: A cross section of a grounded
conducting cylinder in a uniform field.
- Charged Cylinder: A cross section of an uniformly
charged cylinder.
- Charged Hollow Cyl 1: A cross section of an uniformly
charged hollow cylinder. Note that there is no field in the cavity,
since the potential is constant there.
- Charged Hollow Cyl 2: A cross section of an uniformly
charged cylinder with an off-center cylindrical cavity inside. Note that there
is a uniform field in the cavity.
- Floating Cyl + Charge: A cross section of a cylinder
with floating potential, with a charge next to it. The charge on the
cylinder is a constant (zero), so the potential will vary depending on
where the charge is. If the charge is deleted then the cylinder will
be at ground.
- Floating Cyl + Plates: A cross section of a cylinder
with floating potential, with two plates at positive and negative
potentials. The charge on the cylinder is a constant as long as it is
not touching anything, so the potential will vary depending on where
it is located. If you move the cylinder so it is touching one of the
plates, then enough charge will move onto the cylinder to make its
potential the same as the plate it is touching.
- Conducting Box: A conducting box at positive potential.
The field is zero inside, since the potential is constant. Note that
the field is stronger at the corners.
- Sharp Point: A conductor at positive potential,
coming to a sharp point. Note that the field is strongest at the point.
- Corner: The corner of a conductor at positive potential.
- 45 Degrees: A 45 degree corner of a conductor at
positive potential. The field near this corner is stronger than
the field near a 90 degree corner.
- 135 Degrees: A 135 degree corner of a conductor at
positive potential. The field is weaker than near a 90 degree corner.
- Dielectric Cylinder: A dielectric cylinder with a charge
near it.
- Dielectric Cyl + Field: A dielectric cylinder in an external
uniform field.
- Dielectric 1: A charge near a dielectric boundary. Notice
that the field lines bend toward the boundary.
- Dielectric 2: A charge inside a dielectric, near the
boundary. Notice that the field lines bend away from the boundary.
- Dielectric + Dipole: A dipole with a dielectric boundary
between the charges.
- Dielectric Capacitor: Two conducting planes at opposite
potentials with a dielectric between them. The surface charge on the
planes is stronger at the dielectric boundary. You can see the total
charge on each plane by moving the mouse over one of them; the charge
is shown in the lower-left hand corner of the screen. The dielectric
strength can be adjusted by right-clicking on it and selecting "Edit".
This will affect the amount of charge on each plane. The stronger
the dielectric, the more charge on each plane, and the higher the
capacitance between the two planes.
- Conducting Planes w/ Gap: Two conducting planes at opposite
potentials with a gap between them.
- Slotted Conducting Plane: Two grounded conducting planes with a gap
between them, in an external field. Some of the field leaks through the
gap.
- Shielding 1: A grounded conducting box shielding its interior from
an external uniform field.
- Shielding 2: A grounded conducting box shielding its exterior from
a charge inside.
- Box w/ One Live Side: A grounded conducting box with one side
that is at positive potential.
- Quadrupole Lens:
This is an electrostatic quadrupole lens, used to focus particle
beams. It is similar to the magnetic quadrupole lens used in particle accelerators.
It consists of four hyperbola-shaped conductors at
alternating potentials. The field varies linearly along the center line.
The Show popup determines which fields or other quantities to
display, and how to display them.
- Show Electric Field (E): Show the electric field
as arrows. The arrows go from dark green to light green and
then to white as the field gets stronger.
- Show E Lines: Show the electric field as lines. The
color of the lines go from dark green to light green and
then to white as the field gets stronger. The density of the
lines is kept fairly constant, so in order to determine the
field strength you need to look at the color of the lines
rather than how far apart they are.
- Show Potential (Phi): Show the potential; green is
positive, red is negative, and black is ground.
- Show Charge (rho): Show the charge density as
yellow (positive) or blue (negative).
- Show Displacement (D): Show the electric displacement vector.
- Show Polarization (P): Show the electric
polarization vector.
- Show Polarization Charge: Show the
polarization charge density.
- Show E/rho: Show both the electric field and the charge density.
- Show E lines/rho: Show both the electric field lines and the charge density.
- Show E/j: Show the current density in conductors and the
electric field outside of conductors.
- Show E/Potential: Show the electric field and the potential.
- Show E lines/Potential: Show the electric field lines and the potential.
- Show Ex: Show the X component of the electric field.
- Show Ey: Show the Y component of the electric field.
- Show Dx: Show the X component of the electric displacement.
- Show Dy: Show the Y component of the electric displacement.
The Show Equipotentials checkbox draws equipotential lines,
which are lines of constant potential.
The Brightness slider controls the brightness, just like on a
TV set. Also when the brightness is higher it causes more equipotentials
to be drawn.
The Equipotential Count slider allows you to control the number
of equipotentials independently from the brightness.
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.