### Educational Content: Inkjet Printing Process#### Understanding Inkjet PrintingImagine being intrigued by the mechanics of inkjet printing as depicted in the opening storyline of Chapter 22. Fascinated, you persuade your father to take you to his manufacturing plant where you could observe machines that print expiration dates on eggs. Engaging with the technician there, you learn some interesting physics behind the process.#### The Science Behind Ink DropsThe technician explains that each ink drop is created by a combination of a piezoelectric crystal, acoustic waves, and the Plateau–Rayleigh instability, producing uniform droplets. The drops have a known mass of \( m = 1.25 \times 10^{-8} \) g. Although the terminology might seem complex, the key detail you notice is the mass of the drops.#### Electrical Charge and MotionFurthermore, each ink drop is charged with a specific value \( q \) and propelled vertically between parallel deflecting plates at a constant terminal speed of 18.5 m/s. For this process:- The plates are \( \ell = 2.25 \) cm in length.- There is a uniform electric field \( E = 6.35 \times 10^4 \) N/C between the plates.#### Problem to SolveBased on your curiosity, the technician sets a challenge: "If the desired position on the egg for the drop requires that its deflection at the end of the plates is 0.17 mm, what should the charge on the drop be?" To solve this, you make use of the known deflections in the electric field and quickly start working towards the answer.#### Diagram ExplanationThe accompanying diagram is crucial for visualizing the scenario:- **Vertical Arrows**: Represent the continuous vertical motion of the ink drop.- **Parallel Deflecting Plates (Blue)**: Create a uniform electric field \( E \) between them (illustrated by horizontal red lines).- **Electric Field Direction (\( E \))**: Arrows indicate the direction of the electric field which impacts the charged ink drop.- **Ink Drop Path**: Shows the trajectory of the ink drop, demonstrating how it moves through the electric field and deflects.This visual aid helps in comprehensively understanding the effect of the electric field on the trajectory of the ink drops.Understanding this interplay of forces and designing the system to achieve precise deflection underscores the intricate science behind seemingly simple tasks like printing on

3. The time taken by the drop to flow along the length of the plates is

3. You are still fascinated by the process of inkjet printing, as described in the opening storyline for this chapter [Check chapter Introduction of Chapter 22]. You convince your father to take you to his manufacturing facility to see the machines that print expiration dates on eggs. You strike up a conversation with the technician operating the machine. He tells you that the ink drops are created using a piezoelectric crystal, acoustic waves, and the Plateau-Rayleigh instability, which creates uniform drops of mass m = 1.25 × 10-8g. While you don't understand the fancy words, you do recognize mass! The technician also tells you that the drops are charged to a controllable value of q and then projected vertically downward between parallel deflecting plates at a constant terminal speed of 18.5 m/s. The plates are { = 2.25 cm long and have a uniform electric field of magnitude E = 6.35 × 10*N/C between them. Noting your interest in the process, the technician asks you, "If the position on the egg at which the drop is to be deposited requires that its deflection at the bottom end of the plates be 0.17 mm, what is the required charge on the drop?" You %3D quickly get to work to find the answer.

3. You are still fascinated by the process of inkjet printing, as described in the opening storyline for this chapter [Check chapter Introduction of Chapter 22]. You convince your father to take you to his manufacturing facility to see the machines that print expiration dates on eggs. You strike up a conversation with the technician operating the machine. He tells you that the ink drops are created using a piezoelectric crystal, acoustic waves, and the Plateau-Rayleigh instability, which creates uniform drops of mass m = 1.25 × 10-8g. While you don't understand the fancy words, you do recognize mass! The technician also tells you that the drops are charged to a controllable value of q and then projected vertically downward between parallel deflecting plates at a constant terminal speed of 18.5 m/s. The plates are { = 2.25 cm long and have a uniform electric field of magnitude E = 6.35 × 10*N/C between them. Noting your interest in the process, the technician asks you, "If the position on the egg at which the drop is to be deposited requires that its deflection at the bottom end of the plates be 0.17 mm, what is the required charge on the drop?" You %3D quickly get to work to find the answer.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

### Educational Content: Inkjet Printing Process

#### Understanding Inkjet Printing

Imagine being intrigued by the mechanics of inkjet printing as depicted in the opening storyline of Chapter 22. Fascinated, you persuade your father to take you to his manufacturing plant where you could observe machines that print expiration dates on eggs. Engaging with the technician there, you learn some interesting physics behind the process.

#### The Science Behind Ink Drops

The technician explains that each ink drop is created by a combination of a piezoelectric crystal, acoustic waves, and the Plateau–Rayleigh instability, producing uniform droplets. The drops have a known mass of \( m = 1.25 \times 10^{-8} \) g. Although the terminology might seem complex, the key detail you notice is the mass of the drops.

#### Electrical Charge and Motion

Furthermore, each ink drop is charged with a specific value \( q \) and propelled vertically between parallel deflecting plates at a constant terminal speed of 18.5 m/s. For this process:

- The plates are \( \ell = 2.25 \) cm in length.
- There is a uniform electric field \( E = 6.35 \times 10^4 \) N/C between the plates.

#### Problem to Solve

Based on your curiosity, the technician sets a challenge: "If the desired position on the egg for the drop requires that its deflection at the end of the plates is 0.17 mm, what should the charge on the drop be?"

To solve this, you make use of the known deflections in the electric field and quickly start working towards the answer.

#### Diagram Explanation

The accompanying diagram is crucial for visualizing the scenario:

- **Vertical Arrows**: Represent the continuous vertical motion of the ink drop.
- **Parallel Deflecting Plates (Blue)**: Create a uniform electric field \( E \) between them (illustrated by horizontal red lines).
- **Electric Field Direction (\( E \))**: Arrows indicate the direction of the electric field which impacts the charged ink drop.
- **Ink Drop Path**: Shows the trajectory of the ink drop, demonstrating how it moves through the electric field and deflects.

This visual aid helps in comprehensively understanding the effect of the electric field on the trajectory of the ink drops.

Understanding this interplay of forces and designing the system to achieve precise deflection underscores the intricate science behind seemingly simple tasks like printing on

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