Electric Field Lines - Definition, Properties, Attraction, FAQs

Edited By Vishal kumar | Updated on Sep 08, 2024 01:21 PM IST

How to define a field or simply what does a field mean? ‘Field’ is a term referring to a quantity that is defined at each and every point in a space. The electric field at a point in the space around a charge or a system of charges gives us the force that a unit positive test charge would experience, if it is placed at that point, without disturbing the system. Now, the work of the electric field lines is to map this electric field around a charge or a configuration of charges pictorially. So in this article we will learn about ‘what is the physical significance of electric field?’, ‘what are electric field lines?’, ‘what information electric field lines provide us with?’, ‘electric field lines/electric lines of force about negative charge, positive charge, electric dipole and some other configurations’, ‘properties of electric field lines or characteristics of electric field lines’ and ‘differential equation for electric force lines’

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Physical Significance of Electric Field

As we have already discussed that electric field at a point in space around a system /configuration of charges tells us how a unit positive test charge would experience force at that particular point. Now, this field does not depend on the test charge we use to determine the electric field at that particular point. So we can say that by knowing the electric field at any point in space, we can calculate the magnitude and direction of force experienced by a unit test charge at that particular point. The direction of electric field is outwards from a positive charge and it is directed inwards in case of a negative charge. Let E be the electric field intensity at a point r and q0 is the test charge, then F( r)= q0E(r),This is the physical significance of the electric field.

What are Electric Field Lines?

Electric field around a charge or a configuration of charges can be mapped pictorially using the electric field lines, also called the electric lines of forces. It is a mathematical way of visualizing electric fields around a charge or a system of charges placed in a particular configuration. This concept was developed by the physicist Michael Faraday in the 19th Century. Actually, electric field lines are nothing but the path along which a unit positive charge will move if it is placed there and allowed to be free to move. However, for electric field lines definition, we can define electric field line as a path, which can be curved or straight, in an electric field, such that tangent to it at any point gives us direction of the electric field at that point.

Consider the figure-1, given below is an electrostatic line of force. The tangent to the line at point P gives us the direction of electric field Ep and similarly, the tangent to the curved line at point R gives us direction of electric field intensityER.

Tangent to a point on an electric field line gives direction of the electric field. (Fig-1)

Thus, electric field lines provide information about the direction of electric field intensity at a point. Also, the magnitude of the electric field is represented by the density of field lines or the number of electric lines of force in that region. The denser is a region with field lines; more is the magnitude of electric field intensity at that region. Note that these field lines are in all the three dimensions.

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Electric Field Lines About a Charge and Configuration of Charges

Figure-2 shows electric field lines/lines of forces due to a single positive charge. Note the direction of electric field lines. These lines for a single positive point charge are directed radially outwards and extend up to infinity.

Electric field lines radiate outwards in case of single positive point charge (Fig-2)

However, in case of a single negative point charge, the electric field lines are directed radially inwards. See figure-3.

single negative point charge (Fig-3)

Figure-4 shows the electric field lines for a pair of equal and opposite charges, also called an electric dipole. Note the direction of the electric field, it goes from positive to negative charge. These electric field lines show that there is a mutual attraction between the two opposite charges. Hence these are the attractive field lines between the charges.

pair of equal and opposite charges (Fig-4)

Figure-5 shows electric field lines for opposite and unequal charges. The electric field lines are denser towards the charge having larger magnitude.

electric field lines for opposite and unequal charges (Fig-5)

Figure-6 shows electric field lines due to two equal positive charges. These field lines are repulsive in nature. These lines exert lateral pressure on each other and this results in repulsion between the charges. Also, note that there is a neutral point exactly at the middle (point M) where net electric field intensity is equal to zero.

Electric field line (Fig-6)

NCERT Physics Notes:

Similarly, figure-7 shows electric field lines due to two equal negative charges.

shows electric field lines due (Fig-7)

This neutral point shifts from the center position if the charges are unequal where this neutral point is closer to the smaller charge (See figure-8).

Electric Field Patterns for Object (Fig-8)

Some other miscellaneous cases such as representation of the field lines due to 2 equal positively charged rods normal to the page (see fig-9) and due to two rods of linear charge density 2 and –λ respectively, normal to the page ( see fig-10).

Notice the box, it represents the neutral point at the center (Fig-9)

The box denotes the neutral point where the electric field is zero.

As the rods have unequal charge density, the neutral point is not present at the center

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Properties of Electric Field Lines

The properties of electric field lines are-

Electric field lines are always continuous in nature. They are continuous curves but they do not form loops. They start from positive charge or a positively charged body and end at a negative charge or a negatively charged body. In case of a single positive and negative charge, the electric field lines end or start at infinity.
The tangent to an electric field line at any point gives us the direction of the electric field at that particular point.
Two electric field lines of forces never intersect with each other. The reason behind this is, if two lines will intersect with each other, then at that intersecting point, we can draw 2 tangents which will give two directions of electric fields E1 and E2 which is not possible (figure-11). Hence, two electric field lines will never intersect with each other.

This is because if they do, there will be 2 directions of electric field which is not possible at a single point. (Fig-11)

The electric field lines exert a lateral pressure in case of repulsion between like charges.
The electric field lines contract longitudinally in case of attraction between opposite charges.
There is no component of the electric field which is parallel to the surface of the conductor. They are always perpendicular to the surface of a conductor (see fig-12).

Electric field lines on a conductor are always perpendicular at its surface. (Fig-12)

Differential Equations for Electric Force Lines/Electric Field Lines

Suppose r=r(s) represent the force lines. Then, drds will represent the tangent to the force line at every point. Since tangent to the curve at any point represents the direction of the electric field. Therefore,

drds=aE(r),where ‘a’ is a constant.

dxds=aEx ;dyds=aEy;dzds=aEz
dxEx=dyEy=dzEz

This is the differential equation for electric field lines.

Solved Examples Based On Electric Field Lines

Example 1: A long cylindrical shell carries a positive surface charge $\sigma$ in the upper half and a negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in : (figures are schematic and not drawn to scale)

Solution:

Direction of Electric field -Due to a Positive Charge electric field is always away from the charge.

Direction of Electric field

Due to the Negative charge electric field is always towards the charge.

The electric field lines around the cylinder must resemble that due to the dipole.

Example 2: Charges are placed on the vertices of a square as shown. Let $\vec{E}$ be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then

1) $\vec{E}$ changes,V remains unchanged

2) $\vec{E}$ remains unchanged V changes

3) both $\vec{E}$ and V change

4) both $\vec{E}$ and V are unchanged

Solution:

Direction of Electric field

Due to the Positive Charge electric field is always away from the charge.

Direction of Electric field

Due to the Negative charge electric field is always towards the charge.

"Unit positive charge" will be repelled by A and B and attracted by -q and -q downwards in the same direction. If they are exchanged the direction of the field will be opposite. In the case of potential, as it is a scalar, they cancel each other whatever may be their position.

$\therefore$ The field is affected but not the potential.

Example 3: A charged particle is free to move in an electric field. It will travel

1) Always along a line of force

2) Along a line of force, if its initial velocity is zero

3) Along a line of force, if it has some initial velocity in the direction of an acute angle with the line of force

4) None of the above

Solution:

Because E points along the tangent to the lines of force. If the initial velocity is zero, then due to the force, it always moves in the direction of E. Hence it will always move on some lines of force.

Hence, the answer is the option (2).

Example 4: A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in the figure as

1) 1

2) 2

3) 3

4) 4

Solution:

Direction of Electric field

Due to the Positive Charge electric field is always away from the charge.

The electric field is always perpendicular to the surface of a conductor. On the surface of a metallic solid sphere, the electrical field is oriented normally (i.e. directed towards the centre of the sphere).

Example 5: Electric lines of force about negative point charge are

1) Circular, anticlockwise

2) Circular, clockwise

3) Radial, inward

4) Radial, outward

Solution:

Direction of Electric field

Due to the Positive Charge electric field is always away from the charge.

Electric lines' force due to negative charge is radially inward.

Summary

Electric field lines are a way to visualize the influence of electric charges in space. They show the direction a positive test charge would move when placed in the field: away from positive charges and towards negative ones. The density of lines indicates the strength of the field, with closer lines indicating stronger fields. Field lines never cross each other, illustrating how electric fields interact without merging.

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Frequently Asked Question (FAQs)

1. Write one difference between electric field lines and magnetic field lines.

Magnetic field lines and electric field lines, both are continuous but electric field lines do not form closed loops. However, magnetic field lines can form closed loops.

2. Why are electric field lines continuous and cannot have sudden breaks?

In an electrostatic field, a charge experiences a continuous force and hence it moves continuously. If the electric field will have sudden breaks, it will mean that a charge will jump from one point to another point which is not possible.

3. When is an electric field line straight?

Electric field line is straight for a single charge.

4. Why do we get a neutral point in the space between two like charges?

This reason behind this is because the net electric field is zero at that point as the field intensities due to the two charges are equal and opposite at that point.

5. What is the physical significance of electric field lines?

Tangent to electric field lines at any point gives the direction of electric field and the higher is the density of electric field lines, the higher is the magnitude of electric field intensity at that region.