A una lámina muy grande de material aislante se le colocó un...

A una lámina muy grande de material aislante se le colocó un exceso de electrones hasta alcanzar una densidad de carga superficial de $-3,00 \mathrm{nC} / \mathrm{m}^2$. (a) A medida que aumenta la distancia de la lámina, ¿el potencial aumenta o disminuye? ¿Puede explicar por qué sin cálculos? ¿Importa la ubicación de su punto de referencia? (b) ¿Cuál es la forma de las superficies equipotenciales? (c) ¿Cuál es el espacio entre las superficies que difieren en $1,00 \mathrm{~V}$ ?

Key Concepts

Reference Point for Electric Potential

Electric potential is defined up to an arbitrary constant because only differences in potential have physical significance. The choice of a zero or reference potential can shift the absolute value of the potential, but does not affect the relationship between potential differences and the electric field. This concept is crucial when discussing whether the potential increases or decreases with distance, as the emphasis is on the change rather than the absolute values.

Equipotential Surfaces

Equipotential surfaces are locations in space where the electric potential remains constant. In the context of an infinite charged sheet, these surfaces are typically parallel to the sheet because the electric field (which is perpendicular to these surfaces) is uniform. Understanding equipotential surfaces helps in visualizing the electrical environment and is key when solving related problems.

Electric Field of an Infinite Sheet

An infinite charged sheet creates a uniform electric field in the surrounding space. Unlike point charges, where the field magnitude decreases with distance, an infinite plane produces an electric field whose magnitude is constant regardless of the distance from the sheet. This concept is fundamental when analyzing the potential and force in systems with large, uniformly charged surfaces.

Relationship Between Electric Field and Electric Potential

The electric potential is related to the electric field by the negative gradient; that is, the electric field is the spatial rate of change of the potential. In a system where the electric field is constant, such as near an infinite sheet, the potential changes linearly with distance. This relationship underlines the importance of the field in determining how the potential increases or decreases as one moves away from the source.

Transcript

00:02 Hi, in the given problem there is a very large charged metallic plate like shown in this figure.

00:20 The charge density, the surface charge density over this plate is given as minus 3 .00 nanoculum per meter square.

00:34 Now, in the first part of the problem, we have to find what will happen to the potential, electrostatic potential, as the distance is increased from this plate, like this.

00:50 If we are going away from the plate, we have to find what should have happened to the electrostatic potential.

00:59 So as we know, this is the negative charge density.

01:05 So the charge over the plate is negative in nature.

01:23 So the potential of a negative charge will also be negative in itself.

01:46 And we know the potential depends inversely.

02:02 On the distance of observation point from the charge distribution, mathematically we can write it like minus 1 by r means e.

02:38 Sorry, it should be v.

02:44 The potential must be depending on the negative.

02:51 Means the inverse of the distance, the negative of the inverse of the distance.

02:58 Negative because the charge is negative and r always comes in the denominator in the expression for potential.

03:05 Or we can say we depends directly on the distance.

03:12 So as the distance is increased, the potential will increase.

03:17 Hence, as the distance of observation point is increased from the charged plate, the potential is also increased.

03:55 The potential is also increased...

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