Informative line

### Electric Field Lines

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.

# Graphical Representation of Electric Field Lines of Force

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

## Electric Field Lines of Point Charge

• 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.

#### Which point charge has greater magnitude?

A

B

C

D

×

Since, number of field lines are proportional  to magnitude of charge.

Number of field lines are in order by counting

A = 8, B= 12 , C = 8 , D = 10

So, magnitude of charge is in  order :

B > D > C = A

Hence, option B is correct.

### Which point charge has greater magnitude?

A
B
C
D

Option B is Correct

# Properties of Field Lines

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 $$\dfrac{N}{4\pi r^2}$$

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

#### Electric field lines for two surfaces (1) and (2) are shown in figure. Choose the correct option regarding electric field strength and its direction.

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

×

Number of field lines are same but the area of the surface differ.

Area of Surface 1 < Area of Surface 2

Field lines strength is inversely proportional to area of surface when number of field lines are same .

Since, area is in order:

Surface 1 < Surface 2

Hence, field lines strength is in order:

Surface 1 > Surface 2

The electric field vector is always tangent to the electric field lines at each point and its direction is in direction of electric field line.

### Electric field lines for two surfaces (1) and (2) are shown in figure. Choose the correct option regarding electric field strength and its direction.

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

Option A is Correct

# Electric Field Lines Due to Charge Combination of Different Nature at a Near and Far 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).

#### Choose the correct option regarding electric field lines of two point charges +4q and  –q from very far . (3 lines / charge)

A

B

C

D None of these

×

In Option (A)

The configuration is for point near point charges .

Hence, option A is incorrect.

In Option (B)

The number of field lines at +4q charge is same as – q charge . But  since, magnitude of +4q > –q , the number of field lines through +4q should be 4 times the number of field lines at –q charge . Hence, option B is incorrect.

In Option (C)

The configuration is for a far point from point charges because 3 lines / charge is given.

Hence, option C is correct.

### Choose the correct option regarding electric field lines of two point charges +4q and  –q from very far . (3 lines / charge)

A
B
C
D

None of these

Option C is Correct

#### Calculate the ratio of $$q_1$$ and  $$q_2$$ from the  figure.

A $$–\dfrac{7}{15}$$

B $$2$$

C $$\dfrac{4}{3}$$

D $$\dfrac{12}{5}$$

×

Magnitude of charge is proportional to the number of field lines.

Number of field lines at $$q_1 = 7$$ (by convention $$q_1 = -7$$ )

Number of field lines at $$q_2 = 15$$ (by convention $$q_2 = 15$$ )

Hence, ratio of  $$q_1$$ and  $$q_2$$

$$\dfrac{q_1}{q_2} = \dfrac{-7}{15}$$

### Calculate the ratio of $$q_1$$ and  $$q_2$$ from the  figure.

A

$$–\dfrac{7}{15}$$

.

B

$$2$$

C

$$\dfrac{4}{3}$$

D

$$\dfrac{12}{5}$$

Option A is Correct

# Behavioral Properties of Electric Field Lines

1. 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.

#### Which of the following field lines are possible?

A

B

C

D

×

Field lines never cross each other.

So, option (A) is incorrect.

Field lines does not form any closed loop.

Hence, option (B) is incorrect.

Field lines do not make any sharp turn.

Hence, option (C) is incorrect.

Electric field lines are continuous curve.

Hence, option (D) is correct.

### Which of the following field lines are possible?

A
B
C
D

Option D is Correct

# Electric Field Lines Due to Charge Combination of same Nature at a Near and Far 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 .

#### Choose the correct option regarding electric field lines of two point charges (+q each) at a point far away [distance between them is very small (Represents 4 lines / 1C charge )].

A

B

C

D None of these

×

In option A

The electric field lines are for a near point and also field lines cannot terminate at positive charge.

Hence, option A is incorrect.

In option B

The electric field lines are for a near point and also field lines cannot terminate at positive charge.

Hence, option (B) is incorrect.

In option C

The electric field lines of two point charges are viewed from far point  and are similar as electric field lines due to point charge of magnitude 2q.

Hence, option C is correct.

### Choose the correct option regarding electric field lines of two point charges (+q each) at a point far away [distance between them is very small (Represents 4 lines / 1C charge )].

A
B
C
D

None of these

Option C is Correct