Skip to main content
Ch 26: Potential and 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 26: Potential and FieldProblema 15
Capitolo 26, Problema 15

The electric potential along the x-axis is V = 100x2 V, where x is in meters. What is Ex at (a) x=0 m and (b) x=1 m?

Guida verificata passo dopo passo
1
Step 1: Recall the relationship between electric potential (V) and electric field (E). The electric field is the negative gradient of the electric potential. Mathematically, this is expressed as: E_x = -dV/dx, where E_x is the electric field along the x-axis and V is the electric potential.
Step 2: Differentiate the given electric potential function V = 100x^2 with respect to x. The derivative is: dV/dx = 200x.
Step 3: Substitute the value of x = 0 into the expression for E_x. Using E_x = -dV/dx, calculate E_x at x = 0.
Step 4: Similarly, substitute the value of x = 1 into the expression for E_x. Using E_x = -dV/dx, calculate E_x at x = 1.
Step 5: Interpret the results. Note that the electric field is a vector quantity, and its direction is determined by the negative gradient of the potential. Discuss how the values of E_x at x = 0 and x = 1 relate to the behavior of the electric field along the x-axis.

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 Potential

Electric potential, denoted as V, is the amount of electric potential energy per unit charge at a point in an electric field. It is a scalar quantity measured in volts (V) and indicates how much work would be done to move a charge from a reference point to a specific point in the field without any acceleration.
Video consigliato:
Percorso guidato
07:33
Electric Potential

Electric Field

The electric field (E) is a vector field that represents the force experienced by a unit positive charge placed in the field. It is defined as the negative gradient of the electric potential, mathematically expressed as E = -dV/dx. This relationship shows how the electric field is related to the spatial change in electric potential.
Video consigliato:
Percorso guidato
03:16
Intro to Electric Fields

Gradient

In physics, the gradient is a vector that represents the rate and direction of change in a scalar field. For electric potential, the gradient indicates how the potential changes with respect to position. In this context, calculating the gradient of the potential function V = 100x^2 allows us to determine the electric field at specific points along the x-axis.
Pratica correlata
Domanda del libro di testo

Two 3.0-cm-diameter aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 100 V battery. What is the capacitance?

1517
views
Domanda del libro di testo

Light from the sun allows a solar cell to move electrons from the positive to the negative terminal, doing 2.4×10−19 J of work per electron. What is the emf of this solar cell?

1247
views
Domanda del libro di testo

What is the potential difference ΔV34 in FIGURE EX26.14?

64
views
Domanda del libro di testo

A −2.0 V equipotential surface and a +2.0 V equipotential surface are 1.0 mm apart. What is the electric field strength at a point halfway between the two surfaces?

1973
views
Domanda del libro di testo

FIGURE EX26.12 is a graph of V versus x. Draw the corresponding graph of Ex versus x.

80
views
Domanda del libro di testo

How much charge does a 9.0 V battery transfer from the negative to the positive terminal while doing 27 J of work?

204
views