<aside> <img src="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/811391b3-eb9d-4070-8288-1c8575646405/Faraday_cage.png" alt="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/811391b3-eb9d-4070-8288-1c8575646405/Faraday_cage.png" width="40px" /> Faraday cage: a conducting enclosure

• The volume enclosed is “screened” from the outside
• External E-fields do not affect inside the “cavity” </aside>

Properties

In the conductor there are free charges

• E-field inside conductor is 0
• E-field is 0 inside the cavity

A charge inside a Faraday Cage

Consider a charge $q$ inside a cavity within a conductor:

• Negative charge $q'$ will be induced on the inside surface of the cavity

We can infer the following properties:

• $\oint\vec E\cdot \text d \vec A=0$
• The charge enclosed $=0$
• $q'=-q$

If we have multiple cavities they will be screened from each other

Energy stored in Capacitors

• Parallel plate capacitor

$$ C=\frac{\epsilon_0 A}{d} \quad ; \quad \phi=Ed \quad ; \quad U=\frac{\epsilon_0 E^2 V}{2} \quad ; \quad u=\frac{\epsilon_0 E^2}{2} $$

Where: $U$ is potential energy, $u$ is energy density and $V=Ad$ is the volume between the plates

• Spherical plate capacitors

$$ C=\frac{4\pi \epsilon_0 r_a r_b}{r_b-r_a} \quad ; \quad U= \frac{Q^2}{2C}=\frac{Q^2(r_b-r_a)}{8\pi\epsilon_0r_ar_b} $$