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Class XII NCERT textbookChapter 1 · Electric Charges and Fields

Wall of Text. Exercises at end.

A Concept from Same ChapterLearning Path: Electric Field

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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

hero-dem...

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.

hero-dem...

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 $F = q E$ .

hero-dem...

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

hero-dem...

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).

hero-dem...

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?

hero-dem...

AI Worksheet

Field at a Midpoint

Calculate electric field at the midpoint between two charges.

Two point charges,

q_A = 3\text{ }\mu\text{C}

and

q_B = -3\text{ }\mu\text{C}

, are located

20\text{ cm}

apart in vacuum. Solve for the electric field at the midpoint O, and then find the force on a

-1.5\text{ }\mu\text{C}

test charge placed there.

Given Values*

List all given numerical values and their standard SI units.

Principle or Formula*

What physical principle or equation will you use to solve this?

Substitution (Electric Field)*

Calculate the electric field due to each charge at the midpoint and add them.

Calculation (Force on Test Charge)*

Use the net electric field to find the force on a test charge q_test = -1.5e-6 C.

Final Answer*

State your final magnitude and direction for both Field and Force.

hero-dem...

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

hero-dem...

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.

hero-dem...

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 $F = q E$ .

hero-dem...

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

hero-dem...

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).

hero-dem...

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?

hero-dem...

AI Worksheet

Field at a Midpoint

Calculate electric field at the midpoint between two charges.

Two point charges,

q_A = 3\text{ }\mu\text{C}

and

q_B = -3\text{ }\mu\text{C}

, are located

20\text{ cm}

apart in vacuum. Solve for the electric field at the midpoint O, and then find the force on a

-1.5\text{ }\mu\text{C}

test charge placed there.

Given Values*

List all given numerical values and their standard SI units.

Principle or Formula*

What physical principle or equation will you use to solve this?

Substitution (Electric Field)*

Calculate the electric field due to each charge at the midpoint and add them.

Calculation (Force on Test Charge)*

Use the net electric field to find the force on a test charge q_test = -1.5e-6 C.

Final Answer*

State your final magnitude and direction for both Field and Force.

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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?

AI Worksheet

Field at a Midpoint

Calculate electric field at the midpoint between two charges.

Two point charges,

q_A = 3\text{ }\mu\text{C}

and

q_B = -3\text{ }\mu\text{C}

, are located

20\text{ cm}

apart in vacuum. Solve for the electric field at the midpoint O, and then find the force on a

-1.5\text{ }\mu\text{C}

test charge placed there.

Given Values*

List all given numerical values and their standard SI units.

Principle or Formula*

What physical principle or equation will you use to solve this?

Substitution (Electric Field)*

Calculate the electric field due to each charge at the midpoint and add them.

Calculation (Force on Test Charge)*

Use the net electric field to find the force on a test charge q_test = -1.5e-6 C.

Final Answer*

State your final magnitude and direction for both Field and Force.

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?

AI Worksheet

Field at a Midpoint

Calculate electric field at the midpoint between two charges.

Two point charges,

q_A = 3\text{ }\mu\text{C}

and

q_B = -3\text{ }\mu\text{C}

, are located

20\text{ cm}

apart in vacuum. Solve for the electric field at the midpoint O, and then find the force on a

-1.5\text{ }\mu\text{C}

test charge placed there.

Given Values*

List all given numerical values and their standard SI units.

Principle or Formula*

What physical principle or equation will you use to solve this?

Substitution (Electric Field)*

Calculate the electric field due to each charge at the midpoint and add them.

Calculation (Force on Test Charge)*

Use the net electric field to find the force on a test charge q_test = -1.5e-6 C.

Final Answer*

State your final magnitude and direction for both Field and Force.

A Textbook You'll Happily Finish.

Concept of Electric Field

Electric Field Vectors

Electric Field of a Point Charge

Field from Two Charges

Electron Fall in Uniform Field

Test Charge Independence

Field at a Midpoint

Concept of Electric Field

Electric Field Vectors

Electric Field of a Point Charge

Field from Two Charges

Electron Fall in Uniform Field

Test Charge Independence

Field at a Midpoint

Parents and Tutors Know Where to Help.

Confusion To Clarity

Finish One Concept in One Focused Sprint.

AI That Helps You Finish, Not Wander.

Can't read it? Switch it.

Less Reading. More Thinking.

Students. Tutors. Parents. Feel the Difference.

One Plan.The Whole Library.

Concept of Electric Field

Electric Field Vectors

Electric Field of a Point Charge

Field from Two Charges

Electron Fall in Uniform Field

Test Charge Independence

Field at a Midpoint

Concept of Electric Field

Electric Field Vectors

Electric Field of a Point Charge

Field from Two Charges

Electron Fall in Uniform Field

Test Charge Independence

Field at a Midpoint

One Plan.
The Whole Library.