Section 3.1 · Worked examples · 2 of 4
Worked example 3.1.2: Toner on the drum of a laser printer
About the worked examples of Section 3.1
Four short numerical calculations, covering four of the applications of Section 3.1.4. Each one starts from Coulomb's law and . Worked example 3.1.1 uses the line-charge result of Problem 3.1.1 directly, and Worked example 3.1.4 additionally borrows and from circuit theory. The best way to use them is to write down the given quantities, derive the formula yourself, and only then put the numbers in. Numerical constants used throughout (with as in Eq. (1.4.2) of Chapter 1):
Toner on the drum of a laser printer
#cf. Application 3.1.3
Given. A toner particle is a sphere of diameter and density . Tribo-charging gives it a charge-to-mass ratio of . The development field near the drum is about .
Find. the electric force on the particle, and how it compares with its weight.
Both the electric force and the weight act on the same particle. The charge is given per unit mass, so we need the mass first. The ratio then does not depend on the particle size at all.
With radius and density ,
, hence
The ratio of the two forces computed separately, , agrees with the size-independent formula. Units of : , a pure number.
The electric force is about two thousand times the weight, so the particle goes wherever the field sends it and gravity plays no role: the image does not fall off when the drum surface turns downwards. For the same reason the toner image on the paper is held only electrostatically until the fuser melts it into the fibres, which is why fusing is needed to make the print permanent.