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Electrostatics

CSCA Electrostatics study guide organized around the publicly available CSCA syllabus. Practice Physics questions on aicsca.com.

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Topic: Electromagnetism > Electrostatics

1. Introduction: Electrostatic Field

An **Electrostatic Field** is a field created by **stationary charges**. Although invisible, it is objectively real. For the CSCA exam, you must master its two core properties:

1. **Force Property**: Exerts force on charges placed within it (described by **Electric Field Strength**).

2. **Energy Property**: Work is done by the electric force when charges move (described by **Electric Potential**).

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2. Comparison of Three Core Quantities

| Quantity | Symbol | Formula | Vector/Scalar | Physical Meaning | Note |

| :--- | :---: | :---: | :---: | :--- | :--- |

| **Electric Field Strength** | $\vec{E}$ | $E = \frac{F}{q}$ | **Vector** | Strength & direction of the field (Force nature) | Direction is that of force on a positive test charge |

| **Electric Potential** | $\varphi$ or $V$ | $V = \frac{W}{q}$ | **Scalar** | Energy state at a point (Energy nature) | Potential decreases along field lines |

| **Potential Difference** | $U$ | $U_{AB} = V_A - V_B$ | **Scalar** | Difference in potential (Voltage) | $W_{AB} = qU_{AB}$ |

**Note**: $E$ is independent of $F$ and $q$, determined only by the source; similarly, $V$ is independent of $W$ and $q$.

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3. Core Law: Coulomb's Law

Applies to two **point charges** in a **vacuum**.

$$F = k \frac{|q_1 q_2|}{r^2}$$

* **Constant**: $k \approx 9.0 \times 10^9 \, N \cdot m^2 / C^2$

* **Direction**: Like charges repel, opposite charges attract (along the line connecting them).

* **Exam Tip**: Use absolute values of charges to calculate magnitude, and determine direction separately based on signs.

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4. Key Method: Superposition Principle

This is the most critical topic for exams. When dealing with systems of multiple charges:

1. **Field Superposition (Vector Sum)**:

* **Rule**: Parallelogram rule or Orthogonal decomposition.

* **Step**: Calculate the $E$ vector generated by each charge independently, then combine them.

2. **Potential Superposition (Algebraic Sum)**:

* **Rule**: Direct numerical addition.

* **Step**: Calculate $V$ for each charge (keeping the +/- sign), then sum them up.

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5. Typical Example

**Example: Vector Superposition of Electric Fields**

**Problem**: In a vacuum, two point charges $Q_A = +4.0 \times 10^{-8} C$ and $Q_B = -1.0 \times 10^{-8} C$ are fixed at points $A$ and $B$ on the $x$-axis, separated by $0.1m$. Find the electric field strength at the midpoint $C$.

**Solution Steps**:

1. **Model**: $C$ is the midpoint, so $r_{AC} = r_{BC} = 0.05 m$.

2. **Independent Calculation**:

* Field by $A$ at $C$: $E_A = k \frac{|Q_A|}{r^2} = 9.0\times10^9 \times \frac{4.0\times10^{-8}}{0.0025} = 1.44 \times 10^5 \, N/C$. Direction: **Right** (Away from positive).

* Field by $B$ at $C$: $E_B = k \frac{|Q_B|}{r^2} = 9.0\times10^9 \times \frac{1.0\times10^{-8}}{0.0025} = 3.6 \times 10^4 \, N/C$. Direction: **Right** (Towards negative).

3. **Vector Addition**:

* Since $E_A$ and $E_B$ are in the same direction, add them directly.

* $E_C = 1.44\times10^5 + 0.36\times10^5 = 1.80 \times 10^5 \, N/C$, direction is horizontal to the right.

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6. CSCA Common Errors

* **Vector vs. Scalar Confusion**: $E$ fields cannot be added simply by numbers; you must draw diagrams. Potentials $V$ must be added with signs.

* **Scope of $U = Ed$**: Only applies to **Uniform Electric Fields**, where $d$ is the distance parallel to field lines.

* **Field Line Misconception**: Field lines are NOT the trajectory of charge motion. Dense lines mean stronger field.