Facts about charges:

• 2 types of electrical charge: positive and negative
• Charge is conserved
• Charge is quantised, electron charge: $1.60\times10^{-19}$ C
• Charge is Lorentz invariant: speed doesn't affect the charge

Coulomb’s law

$$ \vec{F}=\frac{q_1q_2}{4\pi\epsilon_0r^2}\hat{r} $$

• Force felt $\vec{F}=\sum_i\vec{f_i}$ individual forces

Triboelectric effect

Definition: Rubbing or touching two objects can transfer electrons from one to the other (this phenomena is the triboelectric effect) → static electricity can cause damage to electronics

Induced charge

<aside> <img src="https://em-content.zobj.net/source/microsoft-teams/337/scroll_1f4dc.png" alt="https://em-content.zobj.net/source/microsoft-teams/337/scroll_1f4dc.png" width="40px" /> Rules: Negative charges repeal and opposite charges attract

</aside>

<aside> <img src="https://em-content.zobj.net/source/microsoft-teams/337/battery_1f50b.png" alt="https://em-content.zobj.net/source/microsoft-teams/337/battery_1f50b.png" width="40px" /> Induction: placing a charged particle next to a conductor which is connected to the earth will attract the opposite charge, then if the connection is severed the opposite charges will remain in the conductor, this is induction charging

</aside>

<aside> <img src="https://em-content.zobj.net/source/microsoft-teams/337/coin_1fa99.png" alt="https://em-content.zobj.net/source/microsoft-teams/337/coin_1fa99.png" width="40px" /> Polarisation: placing a charge next to an isolator will cause the bound charges to separate and create a dipole.

</aside>

The electric field

<aside> <img src="https://em-content.zobj.net/source/microsoft-teams/337/sheaf-of-rice_1f33e.png" alt="https://em-content.zobj.net/source/microsoft-teams/337/sheaf-of-rice_1f33e.png" width="40px" /> Field: physical quantity tat has a value at all points in space and time within a system

• E-field and B-field → vector fields that have magnitude and direction
• $\phi$-field → scalar field, has magnitude only </aside>

<aside> <img src="https://em-content.zobj.net/source/microsoft-teams/337/framed-picture_1f5bc-fe0f.png" alt="https://em-content.zobj.net/source/microsoft-teams/337/framed-picture_1f5bc-fe0f.png" width="40px" /> Electric field: if a test charge $q_{test}$ experiences a force $\vec{F}_E$ due to an electric field $\vec{E}$ then $\vec{E}=\frac{\vec{F}E}{q{test}}=\frac{q}{4\pi\epsilon_0r^2}\hat{r}$

</aside>

Electrostatic field line rules

• Field lines point → negative charge
• Density of line → strength of the field
• Lines end at $\infin$ or a charge
• Lines never cross
• follows superposition
• Direction of force depends on field and charge

Sparks from a pointy object

• Electric field is maximum near the point on a pointy conductor
• Air suffer electric breakdown when E-field exceeds $\approx 3\times10^6$ Vm$^{-1}$

Parallel plate capacitor

• $\vec{F}=q\vec{E}$
• $W=qEd$
• $\Delta\phi=\frac{W}{q}$
• $E=\frac{\Delta\phi}{d}$