To Sketch a Continuous Curve of Particles in What Order Should the Following Steps Be Performed
Electric Field Lines: Properties, Field Lines Around Different Charge Configurations
Electric Field Lines: An electric field is a region around a charge where other charges can feel its influence. Mathematically, the electric field at a point is equal to the force per unit charge. It is a vector quantity, i.e., it has both magnitude and direction. For a system of charges, the electric field is the region of interaction surrounding them. But how do we visualize it? Charges can sense the field around them, but we can merely detect it with proper equipment. To allow the pictorial representation of the overall intensity of the field, Micheal Faraday, in the \(19^\rm{th}\) century, came up with the idea of Electric Field Lines.
What is Electric Field Line?
Electric field lines are a presentation of electric field lines on paper. These are the drawings representing electric fields around charged objects using lines and arrows, making them very useful in visualizing field strength and direction. Like all vectors, the electric field can be represented by an arrow with a length proportional to its magnitude and that points in the direction of the net electric field at that point.
- In the sense of the arrows on the lines, a tangent at any point to an electric field gives the direction of the electric field at that point.
- The magnitude of the field is proportional to the number of field lines per unit area passing through a small surface normal to the lines.
- Thus, field lines determine the magnitude, as well as the direction of the electric field. At points where the field lines are closely spaced, the electric field is considered to be stronger, while the points where the field lines are far apart are the points where the electric field is comparatively weaker.
Faraday invented the picture of field lines to develop an intuitive non-mathematical way of visualizing electric fields around charged configurations. Faraday referred to them as "lines of force." This term is somewhat misleading, especially in magnetic fields, which is why they were termed as "field lines" (electric or magnetic).
How are Electric Field Lines Drawn?
To understand how to draw field lines around a point charge, assume a point charge kept at the origin. From this charge, vectors are drawn in the direction of the electric field, with the length of each vector depicting the strength of the electric field at that point.
The electric field due to a point charge varies inversely with the square of the distance of that point from the point charge. Thus, the electric field's vector gets shorter as we move away from the origin in a radially outwards direction.
Each small arrow indicates the force experienced by a unit positive charge kept at the end of each arrow; by connecting the arrows in a direction along a line, we get an electric field line. Similarly, many field lines can be drawn, all pointing outwards from the point charge. This gives us the direction of the electric field.
The density of field lines represents the magnitude of the electric field at that point. Near a charge, the field is stronger; thus, the density of field lines is more, and the field lines are much closer. But as the field gets weaker away from the charge, the density of field lines is less. An infinite number of lines can be drawn to represent the electric field in any region.
In three dimensions, the number of lines per unit cross-sectional area is considered while calculating the density of field lines in a region. As the electric field varies inversely with the square of the distance from a point charge, thus the area enclosing the charge increases as we move away from the charge. The number of field lines crossing the enclosing area remains constant, whatever be the area's distance from the charge.
What are the Properties of Electric Field Lines?
Properties of electric field lines are as follows:
- Field lines start from a positive charge and end on a negative charge.
- Electric field lines move away from the positive electric charge and towards the negative electric charge.
- A tangent drawn at any point on a field line gives the electric field direction at that point.
- Electric field lines enter or exit a charged surface normally.
- Field lines never cross each other because if they do so, then at the point of intersection, there will be two directions of the electric field.
- In a uniform electric field, the field lines are straight, parallel, and uniformly spaced.
- Electric field lines can not pass through a conductor; that's why the electric field inside a conductor is always zero.
- In a charge-free region, electric field lines are continuous curves.
- Electric field lines tend to contract in length due to the force of attraction between two oppositely charged objects.
- Electric lines of force tend to expand laterally, i.e., they tend to separate from each other in the direction perpendicular to their lengths because of the force of repulsion between like charges.
Electric Field Lines Around Different Configurations of Charges
a. Around a Positive Charge: Electric field lines are radially away from the positive charge.
b. Around a Negative Charge: Electric field lines are radially towards the negative charge.
c. Around Two Positive Charges: The pattern of electric field lines between two positive charges of equal magnitude can be shown as:
d. Around Two Negative Charges: The pattern of electric field lines between two negative charges of equal magnitude can be shown as:
e. Around a Positive and Negative Charge: The pattern of electric field due to two equal and opposite charges can be shown as:
Why Electric Field Lines Never Intersect Each Other?
Electric field lines in a region describe the nature of the electric field in a system of charges. They also reveal the direction of electric field strength at a point in a region of space. If the electric field lines intersect, then there must be distinctly two electric fields with different directions. This is impossible as a single location has only one direction and magnitude of the electric field associated with it.
Electric Field: Line or a Curve?
Electric field lines show the pictorial mapping of the electric field around a configuration of charges. An electric field line is, in general, a curve drawn in such a way that the tangent to it at each point is in the direction of the net field at that point. An arrow on the curve is necessary to specify the direction of an electric field from the two possible directions indicated by a tangent to the curve. A field line is a space curve, i.e., a curve in three dimensions.
Where is the Field Stronger at R or at S?
The field lines are denser at places where the field is strong and further apart in the region where the field is weak. Thus, by the closeness or relative density of the field lines at the given points, we can judge the strength of the electric field at that point. To compare the field strength between \(R\) and \(S\), imagine equal and small elements of the area placed at points \(R\) and \(S\) normal to the field lines. The number of field lines in our picture cutting the area elements is proportional to the magnitude of the field at these points. As can be seen from the picture, the field at \(R\) is stronger than at \(S\).
Summary
Electric field lines are a presentation of electric field lines on paper. These are the drawings representing electric fields around charged objects using lines and arrows, making them very useful in visualizing field strength and direction.
Following are the basic properties of electric field lines:
- Field lines start from a positive charge and end on a negative charge.
- Electric field lines move away from the positive electric charge and towards the negative electric charge.
- A tangent drawn at any point on a field line gives the electric field direction at that point.
- Electric field lines enter or exit a charged surface normally.
- Field lines never cross each other because if they do so, then at the point of intersection, there will be two directions of the electric field.
- In a uniform electric field, the field lines are straight, parallel, and uniformly spaced.
- Electric field lines can not pass through a conductor; that's why the electric field inside a conductor is always zero.
- In a charge-free region, electric field lines are continuous curves.
- An infinite number of lines can be drawn to represent the electric field in any region.
FAQs on Electric Field Lines
Q.1. What is an electric field line?
Ans: Electric field lines can be defined as a curve representing the direction of the electric field when a tangent is drawn on it at any point. These are used to diagrammatically realize the presence of an electric field in a given region.
Q.2. What is an electric field?
Ans: An electric field is a region around a charge where similar charges can feel its influence. It is a vector quantity, and it is equal to the force per unit charge acting at the given point around an electric charge.
Q.3. Sketch the electric field lines around two opposite charges, with the magnitude of the negative charge being smaller than the magnitude of the positive charge.
Ans: When a smaller negative charge is placed across a more significant positive charge, the distribution of the field lines will become:
Q.4. Can two electric field lines intersect?
Ans: No, two electric field lines do not intersect. If the electric field lines intersect, then this would mean that we can draw two tangents at their point of intersection. Thus, the electric field intensity at the point will have two directions, which is not possible.
Q.5. Why aren't there any electric field lines inside a conductor?
Ans: There are no electric field lines within a conductor because the electric field inside a conductor is zero.
Q.6. Write a few properties of electric field lines.
Ans: Few general properties of field lines are:
- Electric field lines start from a positive charge and end at a negative charge.
- Field lines do not form closed curves.
- The number of electric field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.
- Electric field lines never intersect.
- If the electric field in a given region of space is zero, electric field lines do not exist.
- In a uniform electric field, the field lines are straight, parallel, and uniformly spaced.
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