Back to NCERT XII - Physics (Part 1)BackConcept

Electric Field

Define electric field, understand its physical significance, and calculate field due to a point charge and system of charges.

8 micro-lessons

Preview · progress not saved — Chapter 1 is free

7dab5eae...

Notes

Concept of Electric Field

Defines electric field and its relation to force.

How do electric forces act across an empty space? To answer this, early scientists introduced the concept of a field.

A charge $Q$ produces an electric field everywhere in its surrounding space. When a second charge $q$ (the test charge) is brought nearby, this field acts on it to produce a force.

1 / 3

adad8a26...

Visuals

Electric Field Vectors

Visual of electric field vectors around positive and negative charges.

rich vibrant illustration, Kurzgesagt-inspired, bold shapes with subtle texturing, saturated but harmonious color palette, strong composition, professional science museum display quality. Two separate scenarios: On the left, a positive point charge with straight arrows radiating radially outwards in all directions. On the right, a negative point charge with straight arrows pointing radially inwards toward the center.

Click to zoom

For a positive source charge $( +Q)$ , the field points away from the charge. For a negative source charge $( -Q )$ , the field points towards the charge.

3de2d618...

Formula Card

Electric Field of a Point Charge

A point charge creates an electric field around it, directed along $\hat{r}$

E (r) = \frac{1}{4 π ε _{0}} \frac{Q}{r ^{2}} \overset{r}{^}

Symbol Meaning

E

— electric field at a point, measured in

N C^{- 1}

Q

— source charge that creates the field, measured in

C

r

— distance from the source charge to the point

\overset{r}{^}

— unit vector showing the direction of the field

ε_{0}

— permittivity of free space

Key Idea

The electric field is produced by the source charge $Q$ . When a test charge $q$ is placed in this field, it experiences a force given by $F = q E$ .

7607e568...

39071393...

Worked Example

Field from Two Charges

Calculates net electric field at three points.

Problem

Two point charges $q_1$ and $q_2$ , of magnitude $+10^{-8}\text{ C}$ and $-10^{-8}\text{ C}$ , respectively, are placed $0.1\text{ m}$ apart. Calculate the electric fields at points A, B, and C shown in Fig. 1.11.

(Note: Point A is the midpoint between the charges. Point B is $0.05\text{ m}$ to the left of $q_1$ . Point C is $0.1\text{ m}$ from both charges, forming an equilateral triangle.)

1 / 5

c6f5f97e...

Worksheet

Electron Fall in Uniform Field

Calculate time of fall in an electric field.

0 of 3 blanks filled

Consider an electron falling from rest through a distance of $1.5\text{ cm}$ in a uniform electric field of magnitude $2.0 \times 10^4\text{ N/C}$ .

(Take $e = 1.6 \times 10^{-19}\text{ C}$ and $m_e = 9.1 \times 10^{-31}\text{ kg}$ )

The field exerts a downward force on the electron with a magnitude of $F = A \times 10^{-15}\text{ N}$ , where $A =$ .

Using Newton's second law, the magnitude of the acceleration of the electron is $a_e = B \times 10^{15}\text{ m/s}^2$ , where $B =$ (round to one decimal place).

Using the kinematic equation for a body starting from rest, the time required for the electron to fall this distance is $t_e = C\text{ ns}$ , where $C =$ (round to one decimal place).

b6020071...

Multiple-Choice quiz

Test Charge Independence

MCQ testing that E is independent of q.

1 / 5

If the test charge $q$ used to measure an electric field $\vec{E}$ at a specific point is doubled, what happens to the magnitude of the electric field at that point?

← previousSuperposition Principle next →Electric Field Lines And Flux

Notes

Concept of Electric Field

Defines electric field and its relation to force.

How do electric forces act across an empty space? To answer this, early scientists introduced the concept of a field.

A charge $Q$ produces an electric field everywhere in its surrounding space. When a second charge $q$ (the test charge) is brought nearby, this field acts on it to produce a force.

1 / 3

Visuals

Electric Field Vectors

Visual of electric field vectors around positive and negative charges.

Click to zoom

For a positive source charge $( +Q)$ , the field points away from the charge. For a negative source charge $( -Q )$ , the field points towards the charge.

Formula Card

Electric Field of a Point Charge

A point charge creates an electric field around it, directed along $\hat{r}$

E (r) = \frac{1}{4 π ε _{0}} \frac{Q}{r ^{2}} \overset{r}{^}

Symbol Meaning

E

— electric field at a point, measured in

N C^{- 1}

Q

— source charge that creates the field, measured in

C

r

— distance from the source charge to the point

\overset{r}{^}

— unit vector showing the direction of the field

ε_{0}

— permittivity of free space

Key Idea

The electric field is produced by the source charge $Q$ . When a test charge $q$ is placed in this field, it experiences a force given by $F = q E$ .

Worked Example

Field from Two Charges

Calculates net electric field at three points.

Problem

(Note: Point A is the midpoint between the charges. Point B is $0.05\text{ m}$ to the left of $q_1$ . Point C is $0.1\text{ m}$ from both charges, forming an equilateral triangle.)

1 / 5

Worksheet

Electron Fall in Uniform Field

Calculate time of fall in an electric field.

0 of 3 blanks filled

Consider an electron falling from rest through a distance of $1.5\text{ cm}$ in a uniform electric field of magnitude $2.0 \times 10^4\text{ N/C}$ .

(Take $e = 1.6 \times 10^{-19}\text{ C}$ and $m_e = 9.1 \times 10^{-31}\text{ kg}$ )

The field exerts a downward force on the electron with a magnitude of $F = A \times 10^{-15}\text{ N}$ , where $A =$ .

Using Newton's second law, the magnitude of the acceleration of the electron is $a_e = B \times 10^{15}\text{ m/s}^2$ , where $B =$ (round to one decimal place).

Using the kinematic equation for a body starting from rest, the time required for the electron to fall this distance is $t_e = C\text{ ns}$ , where $C =$ (round to one decimal place).

Multiple-Choice quiz

Test Charge Independence

MCQ testing that E is independent of q.

1 / 5

If the test charge $q$ used to measure an electric field $\vec{E}$ at a specific point is doubled, what happens to the magnitude of the electric field at that point?