A uniform electric field has magnitude E and is directed in...

A uniform electric field has magnitude $E$ and is directed in the negative $x$ -direction. The potential difference between point $a$ (at $x=0.60 \mathrm{m} )$ and point $b$ (at $x=0.90 \mathrm{m} )$ is 240 $\mathrm{V}$ . (a) Which point, $a$ or $b$ , is at the higher potential? (b) Calculate the value of $E (\mathrm{c})$ A negative point charge $q=-0.200 \mu \mathrm{C}$ is moved from $b$ to $a$ . Calculate the work done on the point charge by the electric field.

Key Concepts

Uniform Electric Field

A uniform electric field is one in which the magnitude and direction of the field are constant throughout the region of interest. This simplification allows for straightforward calculations and analysis since the relationship between the field and potential difference is linear, making it a fundamental concept when studying electrostatics.

Electric Potential Difference

Electric potential difference represents the change in electric potential energy per unit charge between two points in an electric field. It is the work done in moving a unit positive charge from one point to another, and its measurement and calculation are vital for understanding energy changes in electrostatic systems.

Relationship Between Electric Field and Potential Gradient

The electric field is intimately related to the electric potential through the gradient, with the field equal to the negative rate of change of the potential with respect to distance. Mathematically, in one dimension, this is expressed as E = -dV/dx. This relation is key for converting between field strength and potential differences in problems involving electric fields.

Work Done by an Electric Field

The work done by an electric field on a charge as it moves between two points is given by the product of the charge and the potential difference between those points, W = q?V. This concept is crucial in understanding how energy is transferred to or from distributed charges in an electric field and explains phenomena like acceleration or deceleration of charges depending on their sign.

Transcript

00:01 So in this question, we have a uniform electric field e that is directed in the negative x direction.

00:08 So right now i'm assuming this is x.

00:10 So this is directed in negative x.

00:12 And then we have two points a and b.

00:15 So a is x at 0 .6 and b is x at 0 .9.

00:20 So what it means is that b is to the right of a and they have a difference of 0 .3 meters.

00:26 So question a, it asks us which point is at a higher potential? and that can be answered because the direction of the electric field is always pointing from high potential to low potential.

00:38 And here is pointing in the direction of negative x, that is from b to a.

00:43 Because of that, we know that b is at a higher potential.

00:51 Second part asks us to calculate the value of e.

00:55 And that can be done because we know this can...

01:00 So if you have worked through example 18 .4, you know that e equals v over d.

01:10 Or you can also just, without doing that, another thing you can do is to use the definition of potential.

01:17 The definition of potential is potential energy over q.

01:21 Potential energy over q, potential energy, it's a change of v at least.

01:26 And the change of potential energy is a workdown.

01:28 If the workdown is equals to force, which is eq times the d.

01:32 Distance, first time distance.

01:35 That is the work.