Electric Field Lines - Definition, Properties, Attraction, FAQs

What is a Field?

A field is a physical quantity that exists at every point in space.
The electric field at any point tells us the force that a unit positive test charge would experience if placed at that point.

The electric field of a charge does not depend on the test charge used.
If at point $\mathbf{r}$, the electric field is $\mathbf{E}(\mathbf{r})$ and test charge is $\mathbf{q}_{\mathbf{o}}$, then:

$
\mathbf{F}(\mathbf{r})=q_0 \mathbf{E}(\mathbf{r})
$
The direction of the electric field is:

• Outwards from a positive charge
• Inwards toward a negative charge

What are Electric Field Lines Class 12?

Electric field lines (also called lines of force) are imaginary lines used to represent the direction and strength of the electric field.

Electric Field Lines Definition

Electric field lines are imaginary curves whose tangent at any point gives the direction of the electric field at that point.

(Fig-1)

Electric Field Lines Attraction And Repulsion

• The figure 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.

However, in the case of a single negative point charge, the electric field lines are always directed radially inwards.

• The figure below 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.

• The figure given below shows electric field lines for opposite and unequal charges. The electric field lines are always denser towards the charge having a larger magnitude.

• The figure given below shows electric field lines due to two equal positive charges. These field lines are repulsive. 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.

• Similarly, electric field lines are due to two equal negative charges.

• This neutral point shifts from the center position if the charges are unequal where this neutral point is closer to the smaller charge

• Some other miscellaneous cases such as the representation of the field lines due to 2 equal positively charged rods normal to the page and due to two rods of linear charge density 2 and $-\lambda$ respectively, normal to the page.

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

Properties of Electric Field Lines Class 12

The properties of electric field lines are-

• Electric field lines are continuous curves that start at positive and end at negative charges.
• They never form closed loops, because electric fields are not cyclic.
• They never intersect, because field direction at a point is unique.
  
• The tangent at any point gives the direction of E-field.
• Field lines exert lateral pressure showing repulsion between like charges.
• Field lines contract longitudinally showing attraction between opposite charges.
• Field lines are perpendicular to the conductor’s surface.

Rules For Drawing Electric Field Lines

1. The electric field lines direct away from positive charges and towards negative charges.
2. The electric field lines begin on positive charges and end on negative charges.
3. If there is no end opposite charge, they end at infinity
4. The electric field lines should never cross each other
5. No closed loop because electric field lines don't form closed loops
6. The lines are closer when the field is stronger

Electric Field Around a Point Charge

The electric field around a point charge is experienced in a region around a charge where it exerts force on other charges. The magnitude of the charge and the distance from the charge are the two factors affecting the field strength. The electric field at a distance $r$ of a point charge $q$ is

$$
E=\frac{k|Q|}{r^2}
$$

where,

$E$ is the electric field strength
$Q$ is the magnitude of the point charge
$r$ is the distance from the charge
$k$ is the coulomb's constant

Electric Field Between Two-Point Charges

If the electric field at a point due to $Q_1$ is $E_1=\frac{k\left|Q_1\right|}{r_1^2}$ and due to $Q_2$ is $E_2=\frac{k\left|Q_2\right|}{r_2^2}$, then the total electric field $E$ at that point is:

$$
E=E_1+E_2=\frac{k\left|Q_1\right|}{r_1^2}+\frac{k\left|Q_2\right|}{r_2^2}
$$

where,

$E$ is the total electric field at the point
$r_1$ is the distance from $Q_1$ to the point
$r_2$ is the distance from $Q_2$ to the point
$k$ is the coulomb's constant

Differential Equations for Electric Force Lines/Electric Field Lines

Suppose $\mathbf{r}=\mathbf{r}(s)$ represents the force lines. Then, $\frac{d \mathbf{r}}{d s}$ will represent the tangent to the force line at every point. Since the tangent to the curve at any point represents the direction of the electric field, therefore,

$
\frac{d \mathbf{r}}{d s}=\alpha \mathbf{E}(\mathbf{r})
$

$
\text { where } \alpha \text { is a constant. }
$

$\begin{gathered}\frac{d x}{d s}=\alpha E_x, \quad \frac{d y}{d s}=\alpha E_y, \quad \frac{d z}{d s}=\alpha E_z \\ \frac{d x}{E_x}=\frac{d y}{E_y}=\frac{d z}{E_z}\end{gathered}$

This is the differential equation for electric field lines.

Also, read

• NCERT Exemplar Solutions for All Subjects
• NCERT Notes For All Subjects
• NCERT Solutions for All Subjects

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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 the figure given in : (figures are schematic and not drawn to scale)

1)

2)

3)

4)

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 {E}$ be the electric field and V the potential at the center. 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 center 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.