Section 3.1 · Worked examples · 3 of 4
Worked example 3.1.3: Deflecting a drop in an inkjet 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):
Deflecting a drop in an inkjet printer
#cf. Home exercise 3.1.3
Given. A drop of diameter (water, ) leaves the nozzle at carrying . The deflection plates are long and apart, and the uniform field between them is . The product is beyond the end of the plates.
Find. the landing displacement, and whether gravity matters.
This is the cathode-ray-tube calculation of Home exercise 3.1.3 with a drop instead of an electron: a constant transverse force between the plates (a parabola), no force beyond them (a straight line). Note that here is measured from the end of the plates, so the formula of Home exercise 3.1.3 appears with replaced by :
The transverse acceleration and the time spent between the plates are
so the drop leaves the plates displaced by and inclined at the angle :
The drop flies straight, adding
The closed formula quoted at the start gives the same number:
The whole flight lasts , during which gravity alone would displace the drop by
about times less than the electrostatic deflection.
A drop weighing about a tenth of a microgram is moved by a whole character height, and gravity is negligible: the print head works in any orientation, even upside down. Since , the printer chooses the landing point of each drop simply by choosing its charge. Note that already uses three quarters of the half-gap between the plates: this clearance limits the largest charge a drop may carry.