Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

One type of ink-jet printer, called an electrostatic ink-jet printer, forms the letters by using deflecting electrodes to steer charged ink drops up and down vertically as the ink jet sweeps horizontally across the page. The ink jet forms30μm diameter drops of ink, charges them by spraying 800,000 electrons on the surface, and shoots them toward the page at a speed of 20m/s. Along the way, the drops pass through two horizontal, parallel electrodes that are 6.0mmlong,4.0mm wide, and spaced 1.0mm apart. The distance from the center of the electrodes to the paper is 2.0cm. To form the tallest letters, which have a height of 6.0mm, the drops need to be deflected upward (or downward) by 3.0mm. What electric field strength is needed between the electrodes to achieve this deflection? Ink, which consists of dye particles suspended in alcohol, has a density of 800kg/m3 .

Short Answer

Expert verified

The electric field strength needed is7.06x105N/C

Step by step solution

01

Given Information and Formula used

Given :

The diameter of drops of ink : 30μm

Charge on the droplets : 800,000

Speed : 20 m/s.

Dimensions of electrodes : 6.0mmlong,4.0mmwide, 1.0mmapart.

The distance from the center of the electrodes to the paper : 2.0cm.

Height of the tallest letters :6.0mm

The drops are deflected upward (or downward) by :3.0mm

Ink has a density of : 800kg/m3

Theory used :

Mass : m=ρV

Maximum deflection : tanθ=vyvx

Newton's law : v1y=v0y+ay(t1-t0)

Field strength :E=mayq

02

Calculating the maximum deflection

First, we must locate mass :

m=ρV=ρ(4π3r3)=(800kg/m³)(4π3(30x10-6m)3)=9.04x10-11kg

Then there's charge q:

q=(8x105)(1.6×10-19)C=1.28x10-13C

We now have a value for maximum deflection v1y

role="math" localid="1649140142801" tanθ=vyvx=(2mm30mm)=0.15v1y=tanθ(Vx)=0.15(20m/s)=3.0m/s

03

Calculating the required electric field strength needed between the electrodes 

We can now calculate acceleration ay using the following relation:

v1y=v0y+ay(t1-t0)ay=v1y-v0y(t1-t0)=3.0m/s-0m/s6.0×10-320m/s=3.0m/s3.0×10-4say=1.0×104m/s2

Finally, field strength E:

E=mayq=(9.04x10-11kg)(1.0x104m/s2)1.28x10-13C=7.06x105N/C

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Three charges are placed at the corners of the triangle in FIGURE Q23.15. The ++charge has twice the quantity of charge of the two - charges; the net charge is zero. Is the triangle in equilibrium? If so, explain why. If not, draw the equilibrium orientation.

The combustion of fossil fuels produces micron-sized particles of soot, one of the major components of air pollution. The terminal speeds of these particles are extremely small, so they remain suspended in air for very long periods of time. Furthermore, very small particles almost always acquire small amounts of charge from cosmic rays and various atmospheric effects, so their motion is influenced not only by gravity but also by the earth's weak electric field. Consider a small spherical particle of radius r, density ρ, and charge q. A small sphere moving with speed v experiences a drag force Fdrag=6πηrv, where η is the viscosity of the air. (This differs from the drag force you learned in Chapter 6 because there we considered macroscopic rather than microscopic objects.)

a. A particle falling at its terminal speed vtermis in equilibrium with no net force. Write Newton's first law for this particle falling in the presence of a downward electric field of strength E, then solve to find an expression for vterm.

b. Soot is primarily carbon, and carbon in the form of graphite has a density of 2200kg/m3. In the absence of an electric field, what is the terminal speed in mm/s of a 1.0-μm-diameter graphite particle? The viscosity of air at 20°C is 1.8×10-5kg/ms.

c. The earth's electric field is typically (150 N/C , downward). In this field, what is the terminal speed in mm/s of a 1.0 μm-diameter graphite particle that has acquired 250 extra electrons?

11. II A small glass bead charged to +6.0nCis in the plane that bisects a thin, uniformly charged, 10-cm-long glass rod and is 4.0cmfrom the rod's center. The bead is repelled from the rod with a force of 840μN. What is the total charge on the rod?

The surface charge density on an infinite charged plane is -2.0×10-6C/m2 . A proton is shot straight away from the plane at 2.0×106m/s. How far does the proton travel before reaching its turning point?

An electret is similar to a magnet, but rather than being permanently magnetized, it has a permanent electric dipole moment. Suppose a small electret with electric dipole moment 1.0×10-7Cm is 25cmfrom a small ball charged to +25nC, with the ball on the axis of the electric dipole. What is the magnitude of the electric force on the ball?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free