# Properties of electric lines of force

• logearav
In summary, lines of force do not pass through a conductor, they contract longitudinally, and exert lateral pressure on each other.
logearav

## Homework Statement

my textbook mentions the following as properties of lines of forces among other things
They do not pass through a conductor.

They contract longitudinally.

They exert a lateral pressure on each other.
I want clarification on these points
i) Why lines of force do not pass through the conductor?
What is meant by exerting lateral pressure among each other and contracting longitudinally?

## The Attempt at a Solution

I think lines of force represent path taken by the charge, then how can we say that they don't pass through the conductor

Start with a definition of a line of force. It is a line (straight or curved) whose direction (or, if you prefer, the direction of whose tangent) at any point along it is the direction of the electric field strength vector, E, at that point.

This is not, in general, the same as the path a free charge would take. [A free charge would pick up speed and would 'go wide' on bends.]

Now, about inside a conductor... You're clearly studying the electrostatic case. What must be the electric field strength inside a conductor if its free electrons aren't drifting? Can you see how this solves your problem?

Now what about lateral pressure and longitudinal contraction? Well, draw the pattern of lines of force between a small positive charge and a small negative charge. [You do this by vector addition of the fields due to each charge separately, to establish the resultant field direction at a number of points - enough to see what the pattern of lines is going to be.]

Faraday imagined these lines of force as real things, elbowing each other apart, and also under tension, pulling the charges together. If your teacher favours this conception, go along with it. But don't forget that the definition I gave at the beginning is the bedrock.

i understood about lines of force not traveling inside the conductor. but i can't understand lateral pressure and longitudinal contraction,sir? could u elaborate? also thanks for the reply.

Did you manage to sketch the lines of force due to two separated equal and opposite charges? If not you could cheat by googling 'dipole field' and finding an image: makes sure it's an electric dipole rather than a magnetic dipole.

Can you now see from the image why Faraday thought of the lines as elbowing each other apart, and as under tension and pulling together the charges which they join? Physicists don't now regard lines of force as explaining in this way how charges attract each other. It was, though, a hugely important idea, because it suggested that to understand the forces exerted by charges on one another, one needed to consider things going on in the space between the charges.

You should carefully distinguish Faraday's speculative view of lines of force pushing sideways but under tension from the 'hard facts' about lines of force, which can be deduced from their definition and the laws of electromagnetism. For example, pattern of lines of force due to a dipole can be drawn by vectorially adding the fields (given by the inverse square law) for the individual charges, at a number of points. It is also clear from the definition that lines of force can't cross. The dipole field also illustrates the property of lines of force that the closer together they come the stronger the field.

The Faraday picture (lines pushing apart and under tension) is not among these 'hard facts'. In my view, not using it will not harm your understanding of electric fields.

?

I would like to provide clarification on the properties of electric lines of force mentioned in your textbook. Firstly, it is important to understand that electric lines of force are a visual representation of the electric field. They show the direction in which a positive test charge would move if placed in the field. With that in mind, I will address the three properties mentioned in your textbook.

1. Electric lines of force do not pass through a conductor because a conductor is a material that allows charges to move freely. When an electric field is applied to a conductor, the charges within the conductor will redistribute themselves in such a way that the electric field inside the conductor is zero. This means that the electric lines of force cannot pass through the conductor as they are deflected or redirected by the charges within the conductor.

2. The lateral pressure exerted by lines of force on each other refers to the fact that electric field lines tend to repel each other when they are close together. This can be seen in the case of two positive charges placed close to each other. The electric field lines originating from each charge will repel each other, resulting in a lateral pressure between them.

3. The longitudinal contraction of electric lines of force refers to the fact that as they move away from a charged object, the electric field lines become closer together. This is due to the inverse square relationship between distance and electric field strength. As the distance from a charged object increases, the electric field strength decreases, causing the electric field lines to contract.

Overall, it is important to remember that electric lines of force are a visual representation of the electric field and should not be interpreted as physical objects. They help us understand the direction and strength of the electric field, but they do not physically exist. I hope this clarifies the properties of electric lines of force for you.

## What are electric lines of force?

Electric lines of force, also known as electric field lines, are imaginary lines that represent the direction and strength of the electric field around a charged object. They show the path a positive test charge would follow if placed in the electric field.

## What is the significance of the direction of electric lines of force?

The direction of electric lines of force represents the direction of the electric field at any given point. The lines point away from positive charges and towards negative charges, showing the direction a positive test charge would move if placed in the field.

## How are the spacing and density of electric lines of force related?

The spacing between electric lines of force represents the strength of the electric field. The closer the lines are together, the stronger the electric field is at that point. The density of the lines is directly proportional to the strength of the electric field.

## Why do electric lines of force never intersect?

Electric lines of force never intersect because they represent the direction of the electric field at any given point. If they were to intersect, it would mean that the electric field is pointing in two different directions at the same point, which is not possible.

## How do conductors and insulators affect electric lines of force?

Conductors, such as metals, have free electrons that can easily move through the material. This results in the electric field being distributed evenly throughout the material, causing the electric lines of force to be perpendicular to the surface. Insulators, on the other hand, do not allow the free flow of electrons, so the electric field is not distributed evenly and the electric lines of force are not perpendicular to the surface.

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