How a Wimshurst Machine Works

Nicholas A. Masluknick@randombytes.net

October 30, 2008Revised October 14, 2012

The Wimshurst Machine is an electric generator that utilizes electrostaticinduction to generate a large potential difference across two capacitors. Be-fore getting into the details of the Wimshurst Machine, let’s review somebasic electrostatics.

Consider an uncharged conductor that is attached to ground with a wire.If we bring in a positively charged object from infinitely far away and placeit near the grounded conductor, electrons from the ground will flow intothe conductor, and arrange themselves on the surface of the conductor suchthat the total electric field inside the conductor is zero. If we were to dis-connect the wire that attaches the conductor to ground, the electrons thatflowed in from ground are now trapped in the conductor. We can now re-move the positively charged object, and our conductor is left with a netnegative charge. Note that separating the positively charged object from thenegatively charged conductor requires energy.

If our positively charged object is another conductor, we can think of thetwo conductors as forming a capacitor. From

V =Q

C, (1)

we see that as we decrease the capacitance C while holding the differencein charge Q between the conductors fixed, the potential V between the twoconductors must increase. The dependence of the capacitance on the separa-tion of the two conductors is determined by the geometry of the conductors,and while in general this dependence is not given by a simple expression, the

1

capacitance will drop as the conductors are separated. The energy EC storedin the capacitor is

EC =∫

V dQ =∫ Q

CdQ =

Q2

2C. (2)

We see that as we decrease the capacitance while keeping the charge Q fixed,the energy stored in the capacitor will increase. This is the energy we mustsupply to separate the conductors.

With these ideas in mind, let’s now turn to the Wimshurst Machine. Anexample of a typical Wimshurst Machine is shown in Fig. 1. The WimshurstMachine has a pair of counter-rotating dielectric disks with a number of con-ducting patches around the disks. Brushes or sharp Corona wires at oppositeends of the disks connect patches on both disks to two storage capacitors,and a neutralizing bar connects patches at opposite ends of the disks afterthey pass through the capacitor brushes. The ends of the capacitors that arenot connected to the patch brushes are connected to one another, and we canconsider them at ground potential. The ungrounded ends of the capacitorsform the output of the machine, and are connected to a spark gap that fireswhen the potential across the gap is sufficient to cause dielectric breakdownof the air1.

First, let’s just consider one disk of the Wimshurst Machine; let’s takethe one closest to us in Fig. 2. In order for the machine to operate, theremust be some initial charge. In practice there will always be some charge im-balance. Let’s assume the right storage capacitor is positively charged, whilethe left one is negatively charged. If we rotate the disk counter-clockwise, thepatch at A will pick up a positive charge, while the patch at A′ will becomenegatively charged. As we rotate further, the patches will move to B andB′ where they are connected to one another through the neutralizing bar.Because of the proximity of B to the positive charge from the left capacitorat A, and the proximity of B′ to negative charge at A′, as the patches are

1The dielectric strength of air is about 3 × 106 V/m, or in other words, each mmcorresponds to about 3 kV. Sharper electrodes in the spark gap will cause the air to breakdown at lower voltages, as sharper points produce greater electric fields than smootherones. Large ball electrodes will allow the Wimshurst Machine to charge up a great dealbefore the spark gap triggers, while smaller balls will fire earlier given the same separation.The tip of a needle is so sharp that any charge built up will dissipate through Coronadischarge rather than an instantaneous spark (this can be seen as a steady dim purple glownear the tip). Corona discharge also produces a significant amount of ozone (triatomicoxygen), which has a distinctive smell.

2

(a) Front View (b) Back View

(c) Top View

Figure 1: Images of a typical Wimshurst Machine. The differentcolors and shapes of the metal patches on the disks of this particularWimshurst Machine serve no functional purpose. Note that theseare high resolution images, so if you are reading this document inelectronic form you may zoom in on the figures for further detail.

3

Figure 2: Movement of charge.

4

rotated further and disconnect from the neutralizing bar, the patch originallyat B will be left with a negative charge due to induction, while the patchoriginally at B′ will have a positive charge. The potential difference betweenthese two patches is less than the potential difference between the capacitors,so one disk by itself does nothing more than slowly drain the two capacitorsof charge.

When we bring the second disk into the picture, we can think of it asinitially undergoing the same sort of process as the first disk described above.If we now look at the patch at position B of the frontmost disk, it not onlypicks up a negative charge through induction by the proximity to the rightcapacitor, but it is also influenced by the positive charge on the patch directlybehind it on the rear disk (in fact, most of the charge developed throughinduction is from the influence of patches on the opposite disk). The samething happens at position B′ with the sign of the charges reversed. When wecrank further, we separate the patches from the two disks at position B (andB′), and this action is the same as separating the conductors of a capacitor.Thus by cranking the patches apart, we are adding energy to the system,and increasing the potential difference between the patches on the two disks.This potential difference becomes greater than the potential between the twostorage capacitors, so by the time the patches reach the capacitor brushesthey are able to contribute additional charge to the storage capacitors. Whenthe patches on the front disk reach positions C and C ′, they contribute tothe induction of charge on the patches of the rear disk at these positions,the same way the rear patches contribute to induction to the front disk’spatches at B and B′. As the storage capacitors charge up, the charges andvoltages developed through induction and separation of patches increases. Itis important that the disks be rotated in the correct direction; rotating in theopposite direction will only be effective at neutralizing the storage capacitors.

5