Skip to main content
Ch 31: Electromagnetic Fields and Waves
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 31: Electromagnetic Fields and WavesProblema 9
Capitolo 31, Problema 9

Show that the quantity ϵ0(dΦe/dt) has units of current.

Guida verificata passo dopo passo
1
Step 1: Begin by identifying the physical quantities involved. Here, ϵ₀ represents the permittivity of free space, dΦₑ/dt is the rate of change of electric flux, and we need to show that the product ϵ₀(dΦₑ/dt) has units of current.
Step 2: Recall the SI unit of permittivity of free space (ϵ₀). It is measured in farads per meter (F/m). A farad (F) is equivalent to coulombs per volt (C/V), so ϵ₀ has units of C/(V·m).
Step 3: Consider the electric flux Φₑ. Electric flux is defined as the integral of the electric field over an area, Φₑ = ∫E·dA. The electric field (E) has units of volts per meter (V/m), and area (A) has units of square meters (m²). Therefore, Φₑ has units of V·m.
Step 4: The rate of change of electric flux, dΦₑ/dt, involves dividing the units of Φₑ (V·m) by time (seconds, s). Thus, dΦₑ/dt has units of V·m/s.
Step 5: Multiply ϵ₀ (C/(V·m)) by dΦₑ/dt (V·m/s). The units become (C/(V·m)) × (V·m/s) = C/s. Since coulombs per second (C/s) is the unit of electric current, this demonstrates that ϵ₀(dΦₑ/dt) has units of current.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Concetti chiave

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

Electric Flux (Φe)

Electric flux (Φe) is a measure of the electric field passing through a given area. It is calculated as the product of the electric field (E) and the area (A) through which it passes, taking into account the angle between the field lines and the normal to the surface. The unit of electric flux is the volt-meter (V·m), which can also be expressed in terms of base SI units as kg·m²/(s³·A).
Video consigliato:
Percorso guidato
05:43
Electric Flux

Permittivity of Free Space (ϵ0)

The permittivity of free space (ϵ0) is a fundamental physical constant that characterizes how electric fields interact with the vacuum of space. It has a value of approximately 8.85 x 10^-12 F/m (farads per meter) and is crucial in determining the capacitance of capacitors and the behavior of electric fields in free space. This constant plays a key role in Maxwell's equations, which describe electromagnetism.
Video consigliato:
Percorso guidato
5:05
Spinning Space Station

Current (I)

Electric current (I) is the flow of electric charge through a conductor, typically measured in amperes (A). One ampere is defined as one coulomb of charge passing through a point in a circuit per second. In the context of the equation, showing that ϵ0(dΦe/dt) has units of current involves demonstrating that the units of the expression correspond to those of amperes, linking electric flux change over time to charge flow.
Video consigliato:
Percorso guidato
05:38
Intro to Current
Pratica correlata
Domanda del libro di testo

What capacitance, in μF, has its potential difference increasing at 1.0×106 V/s when the displacement current in the capacitor is 1.0 A?

73
views
Domanda del libro di testo

The electric field of an electromagnetic wave in a vacuum is Ey=(20.0 V/m)cos[(6.28×108)x−ωt]E_y = (20.0 \(\text{ V/m}\)) \(\cos\)[(6.28 \(\times\) 10^8)x - \(\omega\) t], where x is in m and t is in s. What are the wave's magnetic field amplitude?

206
views
Domanda del libro di testo

A 10-cm-diameter parallel-plate capacitor has a 1.0 mm spacing. The electric field between the plates is increasing at the rate 1.0×106 V/m s. What is the magnetic field strength on the axis?

77
views
Domanda del libro di testo

A radio receiver can detect signals with electric field amplitudes as small as 300 μV/m. What is the intensity of the smallest detectable signal?

132
views
Domanda del libro di testo

A rocket zooms past the earth at v=2.0×106 m/s. Scientists on the rocket have created the electric and magnetic fields shown in FIGURE EX31.4. What are the fields measured by an earthbound scientist?

1408
views
Domanda del libro di testo

The magnetic field of an electromagnetic wave in a vacuum is Bz=(3.0 μT)sin[(1.00×107)x−ωt]B_{z}=(3.0\(\text{ }\)\(\mu\) T)\(\sin\)[(1.00\(\times\)10^7)x-\(\omega\) t], where x is in m and t is in s. What are the wave's wavelength?

216
views