Figure 18.42 shows a set of electric-field lines for a particular distribution of charges. Use t

Figure 18.42 shows a set of electric-field lines for a...

Key Concepts

Relationship between Electric Field and Equipotentials

There is a fundamental relationship between electric field lines and equipotential surfaces: the electric field is always perpendicular to equipotential surfaces. This perpendicularity is used to draw equipotential lines based on the configuration of the field lines, helping to accurately represent regions of equal potential.

Charge Distribution

The charge distribution refers to how electric charges are arranged in space, which determines the pattern of the electric field lines. Understanding the underlying charge distribution aids in interpreting both the field lines and the corresponding equipotential surfaces, as both are directly influenced by how charges are placed.

Equipotential Surfaces

Equipotential surfaces are imaginary surfaces (or curves in two dimensions) where the electric potential is the same at every point. No work is needed to move a charge along an equipotential surface because the potential difference is zero. They provide a complementary way to visualize the electric field.

Electric Field Lines

Electric field lines are a visual tool used to represent both the direction and the magnitude of the electric field. The density of these lines indicates the field strength, and their arrowheads show the field direction (from positive to negative). They help in understanding how charges influence the surrounding space.

Transcript

00:01 This question, we are given this configuration and we are told that it's a set of electric field lines.

00:06 And we're asked to use these lines to draw a series of equal potential.

00:11 So let's try to just do it.

00:16 Because for equal potential, you just draw lines that is perpendicular to the electric field lines.

00:23 A seventh thing is that equipotentials, a couple of things about equal potentials.

00:28 Firstly, it's always perpendicular to the electric field.

00:33 Second, never intersects.

00:40 Third is that it should be denser when electric field is larger.

00:50 Or in other ways, when the electric field lines are denser too.

00:54 So let's draw the easiest one is in the middle when it's particular to everything.

01:02 Is that because it has to be perpendicular? and i want to look always be funicular, so it might be something like this and that gradually changes.

01:29 Actually we only know here.

01:40 Actually here pretty much from here we are already seeing it already look a little bit suspicious because are they not going to intersect? maybe they will intersect but of course we can imagine that maybe they go this where they don't intersect as possible there's a possibility so this is check never intersect maybe but the last one is they has to be denser when the electric field is large the electric field seems the field line seems to be denser here but given the direction of the electric field it does not look like the equal potential plane can be denser over here because they're going in this direction.

02:26 So like this part will be, let me try to clean this up a little bit.

02:32 This part will be denser than this part.

02:35 Just because it has to be in this shape.

02:38 And given this shape, it will converge at the bottom of the page.

02:42 So it does not look like it is possible for the equipotential plane to be denser when the electric field lines answer.

02:52 It does not satisfy this requirement.

02:56 So what that means is that this electric field is just not possible to have an electric field like this.

03:04 This is a this question is not possible.

03:08 So and that's what you should write.

03:09 You should write that this is a trick question...