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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.

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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.

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Electric field lines point radially outward from a positive charge and inward toward a negative charge.

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Electric Field Formula

Formula for E-field of a point charge.

Electric Field of a Point Charge

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

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

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 $F = q E$ .

For a positive source charge, the field points away from the charge. For a negative source charge, the field points towards the charge.

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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.)

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Worksheet

Electron Fall in Uniform Field

Calculate time of fall in an electric field.

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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).

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quiz

Test Charge Independence

MCQ testing that E is independent of q.

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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?