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Electric Field Strength

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

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Topic: Electromagnetism > Electrostatics > Electric Field Strength

1. Core Concept: What is Electric Field Strength?

**Electric Field Strength ($\vec{E}$)** is a vector quantity that describes the **strength** and **direction** (force property) of an electric field.

* **Definition**: The ratio of the electric force $\vec{F}$ experienced by a **test charge** placed at a point to its charge $q$.

* **Formula**:

$$\vec{E} = \frac{\vec{F}}{q}$$

* **Unit**: Newton/Coulomb ($N/C$) or Volt/Meter ($V/m$).

* **Direction**: Defined as the direction of the force on a **positive** test charge.

**CSCA Critical Point**:

The field strength $\vec{E}$ is an intrinsic property of the field, determined **only by the source charge**. It is **independent** of the test charge $q$.

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2. Core Formulas and Applications

| Scenario | Formula | Note |

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

| **Definition** | $\vec{E} = \frac{\vec{F}}{q}$ | Valid for **any field**. $q$ is the test charge. |

| **Point Charge** | $E = k \frac{|Q|}{r^2}$ | Valid only for **point source $Q$**. Direction: Outward for (+), Inward for (-). |

| **Uniform Field** | $E = \frac{U}{d}$ | Valid only for **uniform fields** (e.g., capacitor plates). $d$ is distance **along the field lines**. |

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3. Core Method: Superposition Principle

When multiple source charges exist, the net field at a point is the **vector sum** of the individual fields produced by each charge.

**Steps**:

1. **Calculate Magnitude**: Use $E = k|Q|/r^2$ for each charge.

2. **Determine Direction**: Draw vectors based on "Out for Positive, In for Negative".

3. **Vector Addition**: Use the Parallelogram Rule or Orthogonal Decomposition.

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4. Typical Examples (Revised)

**Example 1: Point Charge Calculation**

**Problem**: A source charge $Q = +4.0 \times 10^{-8} C$ is in a vacuum. Find $E$ at distance $r = 0.2 m$.

**Solution**:

* Magnitude: $E = 9.0 \times 10^3 \, N/C$.

* Direction: Since $Q$ is positive, radially **outward**.

**Example 2: Superposition (Dipole Model)**

**Problem**: Charge $+q$ is at $A$ and $-q$ is at $B$. Find the direction of the electric field at point $P$ on the **perpendicular bisector** of $AB$.

**Solution**:

1. **Analyze Vectors**:

* $\vec{E}_A$ (from $+q$): Points away from $A$ (Up-Right).

* $\vec{E}_B$ (from $-q$): Points towards $B$ (Down-Right).

2. **Vector Decomposition**:

* **Vertical Components**: Equal magnitude, opposite direction $\rightarrow$ **Cancel out**.

* **Horizontal Components**: Same direction (Right) $\rightarrow$ **Add up**.

3. **Conclusion**: The net field is **Horizontal to the Right** (Parallel to line $AB$).

**Example 3: Uniform Field**

**Problem**: Voltage between plates is $100V$, distance is $2cm$. Find $E$.

**Solution**:

Convert units: $d = 0.02m$.

$$E = \frac{U}{d} = \frac{100}{0.02} = 5000 \, V/m$$