Skip to main content
Ch 23: The Electric Field
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 23: The Electric FieldProblema 73
Capitolo 23, Problema 73

A proton orbits a long charged wire, making 1.0×1061.0×10^6 revolutions per second. The radius of the orbit is 1.01.0 cm. What is the wire's linear charge density?

Guida verificata passo dopo passo
1
Start by identifying the force acting on the proton. The centripetal force required to keep the proton in circular motion is provided by the electrostatic force between the proton and the charged wire. The centripetal force is given by: Fc = mv2/r, where m is the mass of the proton, v is its velocity, and r is the radius of the orbit.
The electrostatic force between the proton and the charged wire is given by: Fe = qE, where q is the charge of the proton and E is the electric field due to the charged wire. For a long charged wire, the electric field at a distance r is given by: E = 2kλ/r, where λ is the linear charge density and k is Coulomb's constant.
Equate the centripetal force to the electrostatic force: mv2/r = q(2kλ/r). Simplify the equation to solve for λ: λ = (mv2)/(2kq).
Determine the velocity of the proton. The proton completes 1.0 × 106 revolutions per second, so its angular velocity is ω = 2π(1.0 × 106). The linear velocity is related to the angular velocity by v = ωr. Substitute the radius r = 0.01 m to find v.
Substitute the known values into the expression for λ. Use m = 1.67 × 10-27 kg (mass of a proton), q = 1.6 × 10-19 C (charge of a proton), k = 8.99 × 109 N·m2/C2, and the calculated value of v. Solve for λ.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
14m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Centripetal Force

Centripetal force is the net force acting on an object moving in a circular path, directed towards the center of the circle. For a charged particle like a proton orbiting a charged wire, this force is provided by the electric field created by the wire. The balance between the centripetal force required for circular motion and the electric force due to the wire's charge is crucial for determining the wire's charge density.
Video consigliato:
Percorso guidato
06:48
Intro to Centripetal Forces

Electric Field and Force

The electric field around a charged object exerts a force on other charges within that field. For a long charged wire, the electric field can be calculated using Gauss's law, which relates the electric field to the linear charge density. The force experienced by the proton due to this electric field is what keeps it in circular motion, allowing us to relate the charge density to the proton's orbit.
Video consigliato:
Percorso guidato
03:16
Intro to Electric Fields

Linear Charge Density

Linear charge density is defined as the amount of electric charge per unit length along a charged object, such as a wire. It is denoted by the symbol λ (lambda) and is measured in coulombs per meter (C/m). In this problem, calculating the linear charge density of the wire involves using the relationship between the electric field produced by the wire and the centripetal force acting on the proton in its circular orbit.
Video consigliato:
Percorso guidato
8:13
Intro to Density
Pratica correlata
Domanda del libro di testo

A rod of length L lies along the y-axis with its center at the origin. The rod has a nonuniform linear charge density λ=a∣y∣ λ=a|y|, where a is a constant with the units C/m2. Find the electric field strength of the rod at distance x on the x-axis.

110
views
Domanda del libro di testo

An infinitely long sheet of charge of width L lies in the xy-plane between x = -L /2 and x = L /2. The surface charge density is h. Draw a graph of field strength E versus x for x > L /2.

448
views
Domanda del libro di testo

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 forms 30-μm-diameter drops of ink, charges them by spraying 800,000 electrons on the surface, and shoots them toward the page at a speed of 20 m/s . Along the way, the drops pass through two horizontal, parallel electrodes that are 6.0 mm long, 4.0 mm wide, and spaced 1.0 mm apart. The distance from the center of the electrodes to the paper is 2.0 cm. To form the tallest letters, which have a height of 6.0 mm, the drops need to be deflected upward (or downward) by 3.0 mm. 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 800 kg/m3.

1681
views
1
rank