Question

In class I demonstrated a little gizmo that allows the levitation of a little mylar shape.

Estimate (to an order of magnitude or so) the charge of the mylar shape, expressed in

a number of extra (or missing) electrons. Then give the approximate fraction of the

total number of electrons in the mylar shape that this comprises.

Some notes to help:

Balance between repulsive electric force and gravity is the key thing here. Neglect

air resistance – even though it’s significant, it’s nonetheless zero when the thing

is levitating.

Assume the mylar is 0.1mm thick and has a density of 1 g/cm^3. The piece I used

was around 10×5 cm.

Please be clear with diagrams and units.

The amount of external field is not given in the problem. All that is given to solve the problem is written here. The answer can be an estimation, doesnt have to be exact.

Answer 1

The free body diagram of the force on the floating sheet is given below:

When this two forces becomes equal, the sheet floats. Now if we know the gravitational force on the sheet, the electrostatic force is equal to that. For units we convert everything into SI.

Total mass of the sheet = its volume * its density = area*thickness*density =

F =

Gravitational Force on the sheet = Electrostatic force on the sheet =

As in many cases of electrostatic repulsion, charges repel in pair. So we can make a liberated guess is that it gets repelled by the field caused by the same magnitude of charge Q and a standard repulsion distance r = 0.3m is assumed, So the Coulomb's law in this case is,

(k is Coulomb's constant)

so the estimated number of extra (or missing) electrons = Q/charge of a single electron = 4.375*10¹² .

______________________________________________________________________

Mylar is made of polyethylene terephthalate, (C₁₀H₁₂O₆), which has approximate molar mass of 228g = 0.228kg. and a molecule of that contains 12*10 + 12 + 8*6 = 180 electrons

So 0.228kg mylar contains roughly 6.023*10²³ atoms,

Therefore 0.005kg will contain = mylar molecules, so

electrons,

So the fraction of of extra (or missing) electrons is =

________________________________________________________________

Note: the determined charge without knowing the filed is somewhat of a crude estimation. Also mylar has no constant molecular weight, the quantity is estimated from its mother-material polyethylene terephthalate. It shows a far fetched assumption, but helps to get a picture and idea around this concept.

_______________________________________________________________