Learn properties of electric field lines definition, practice graphical representation of electric field lines of force and electric field lines due to charge combination of same nature at a near and far point.

- The graphical representation of electric field in a region is represented by drawing certain lines. These lines are electric field lines of force.

- The electric field lines for a point charge are drawn radially from the source charge.
- It is distributed spherically around.
- For a positive point charge, they are drawn radially outward.

- For a negative point charge , they are drawn radially towards the source.

**Note : - **Electric field lines shown in figure are radially distributed in spherical 3 –D shape.** **

- Number of field lines is directly proportional to the value of source charge.
- If 8 lines represent 1C charge , Then 16 lines represent 2C charge.

**1) **The electric field vector** \((\vec E)\)** is tangent to the electric field line at each point and its direction is given by the direction of field line.

**2)** Number of field lines per unit area is proportional to the strength of the electric field.

- Consider an imaginary spherical surface of radius \(r\) concentric with a point charge.
- Then, electric field lines density will be \(\dfrac{N}{4\pi r^2}\)

\(\implies E\propto\dfrac{N}{4\pi r^2}\)

A Electric field strength at (1) is more than (2) and direction of \((\vec E_1)\) is correct

B Electric field strength at (1) is more than (2) and direction of \((\vec E_2)\) is correct

C Electric field strength at (2) is more than (1) and direction of \((\vec E_1)\) is correct

D None of these

- Electric field lines are continuous curve and tangent to these field lines gives direction of electric field at that point.

**2) ** Electric field lines begin from positive charge and terminate at negative charge.

**3) ** Number of field lines that begin from positive charge and terminating at negative charge is proportional to the magnitude of charge.

**4) ** Number of field lines per unit area is proportional to the field strength. It means denser the field , greater the field strength at that point . Since, field lines are denser at surface 1 . So, field strength is greater at surface 1.

**5) ** Electric field lines make no sharp turn because then tangent at that point is undefined and hence electric field vector is also undefined .This type of electric field lines is not possible.

**6) **Electric field lines do not form closed loop as they begin at positive charge and terminate at negative charge.

**7) ** Electric field lines do not intersect each other because then electric field vector will have two directions at that point.

- Consider two point charges of equal magnitude , kept in vicinity of each other.
- At any point near to point charges, effect of respective charges will be dominant. Hence, field lines very close to them are nearly radial.
- At point A, effect of charge \(q_1\) is dominant as it is near to it and at point B, effect of charge \(q_2\) is dominant as it is near to \(q_2\) . But at point C, effect of both charges is equal.

- For a point, very far from these two point charges, the field will be same as field due to point charge of magnitude 2C at that point because even a galaxy seen from very far, seems as a point .

- Consider two point charges of +3q and –q respectively, as shown in figure.

- The number of field lines leaving +3q charge is one-third the number of field lines terminating at –q charge . Hence, only one-third of the lines reach –q charge.
- For a near point , the configuration of electric field lines is as shown in figure.

- For a point very far from point charges , the electric field lines are same as field lines from charge (+2q).

A \(–\dfrac{7}{15}\)

B \(2\)

C \(\dfrac{4}{3}\)

D \(\dfrac{12}{5}\)