Electric Fields

### Forces on charges

* Electric charge **Q**  is measured in **coulombs (C)** and can be either positive (carried by particles like protons) or negative (carried by particles like electrons)
* The smallest unit of charge is **1.6 × 10^-19C** (the size of the charge on an electron or proton)
* **Oppositely** charged particles **attract** each other. **Like** charges **repel**.(The force experienced is given by **Coulomb's Law**)

### Calculate forces using Coulomb's Law

* **F=kQ1Q2/r^ 2**
* **F** is the force on either charge (N)
* **Q1** and **Q2** are the two charges (C)
* **r** is the separation of the centres of the two charges (m)
* **k** is a constant; its value is **9 × 10^9** Nm^2 C^-2
* **k = 1/(4πε0 )**, where **ε0** is the permittivity of free space.

### Electric Field Strength

* **Electric field strength** ,**E**, is defined as the **force per unit positive charge**.(It's the force that a charge +1 C would experience if it was placed in the electric field.)
* **E=F/Q**

Where **E** is electric field strength(NC^-1)， **F** is the force(N) and **Q** is the charge (C)

* Note that since force is a vector and charge is a scalar, **electric field strength** must be a **vector**.(pointing in the **direction** that a **positive charge** would **move**)

### Representing electric fields

Fields are represented by drawing field lines **(lines with arrows)**

* The **closer** together the lines are the **stronger** the field.
* Field lines point in the **direction** a **positive test charge** would **move**.

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### Types of electric field

Point charges

* A **point charge**, or any body that behaves as if all its charge is concentrated at the centre, has a **radial** field.

The electric field for such a charge can be found from Coulomb's law **F=kQq/r^2** **F = qE** This gives **E=kQ/r^2**

Parallel plate capacitor

* A **uniform field** can be produced by connecting two **parallel plates** to the opposite poles of a battery

* In a **uniform field** , the field lines are **parallel** so they're always the **same distance** apart. This means that the **field strength** is the **same** **at all points** within the field ( a test charge would experience the **same** **force** wherever it was.)

* The **field strength** between two **parallel plates** depends on the **potential difference**, **d** , between them, according to the equation **E=V/d** (**V** is the potential difference between the two plates. **d** is the distance between plates. This shows that electric field strength can also have units of **V m^-1**)

### Variation of field with distance

Point charge

* The decline of **E** with **distance** follows an **inverse square law** (**E ∝ 1/r^ 2)**

Parallel plate capacitor

* **E** is **constant** whatever the position between the plates

### Electric potential

* **potential difference** - a potential difference between two points means there is a **voltage drop** between them. Accordingly, electrical potential is measured in **volts**.
* The **potential** at a point in an electric field is defined as the **work done** in bringing **a test unit positive** **charge** from **infinity** to that point.(**The potential of a charge at infinity** is always defined to be **zero**.)
* The definition of **potential** in terms of **work** tells us that electric potential is a measure of the **potential** **energy per unit charge**(The potential energy on a charge due to a potential V is: **P.E. = qV P.E.** = potential energy (J) **q** = charge (C) **V** = electric potential (V)
* Since energy is a scalar and charge is a scalar, potential must also be a **scalar quantity.** The work done when a charge moves through a potential difference is given by **W = Q∆V** **W** = work done (J) **Q** = charge (C) **∆ V** = potential difference (V)
* The electrical potential energy **increases** if a **positive charge** moves to a point of **higher potential** or a **negative charge** moves to a point of **lower potential**

### Potential for point charge, parallel plate capacitor

* For a **point charge Q** **V =kQ/r**
* For a **parallel plate capacitor** with spacing **d** and potential difference **V** between the plates, the potential **decreases** **linearly** between the positive and negative plates