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Charging Ink Droplets · Physics Playground

Exercises Electric charge and fields

Example from Physics, 18.1 Electrical Charges, Conservation of Charge, and Transfer of Charge

Charging Ink Droplets

Electrically neutral ink droplets in an ink-jet printer pass through an electron beam created by an electron gun, as shown in Figure 18.14. Some electrons are captured by the ink droplet, so that it becomes charged. After passing through the electron beam, the net charge of the ink droplet is $q_{ink drop} = −1 \times 10^{−10} C$ . How many electrons are captured by the ink droplet?

Six small purple spheres, each marked as “e superscript minus”, are arranged vertically and labeled as “electrons”. The three lowest spheres are enclosed in a rectangle, the fourth one above them is crossing the upper edge of the rectangle, and the two uppermost spheres are outside the rectangle. An arrow next to the two uppermost spheres is pointing upward, suggesting the direction of movement of the purple spheres. A much larger black sphere, labeled “Ink droplet”, is above and to the left of the column of purple spheres, and an arrow pointing toward the right suggests the direction of movement of the black sphere.

Figure 18.14 Electrons from an electron gun charge a passing ink droplet.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
A single electron carries a charge of $q_{e^{-}} = −1.602 \times 10^{−19} C$ . Dividing the net charge of the ink droplet by the charge $q_{e^{-}}$ of a single electron will give the number of electrons captured by the ink droplet.
Solution
The number n of electrons captured by the ink droplet are

$n = \frac{q_{ink drop}}{q_{e^{-}}} = \frac{- 1 \times 10^{- 10} C}{- 1.602 \times 10^{- 19} C} = 6 \times 10^{8} .$
18.4

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From Physics (1st edition) by OpenStax (Rice University), section 18.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.

Strategy

Solution