- Suppose two electric charges $Q_{1}$ and $Q_{2}$ in space are separated by d, and the electric field force they want to interact with.
- Now take $Q_{1}$ as the center of the circle and $d$ as the radius to make the ball. According to the Gaussian law, the electric flux on the sphere is only related to the amount of charge in the sphere, which is $\frac{Q_{1}}{\varepsilon_0}$ in this example.
- Divide the electric flux in the above formula by the surface area to get the electric field intensity $\frac{Q_{1}}{4\pi d^{2}\varepsilon_0}$
- Field strength is multiplied by $Q_{2}$ to get Coulomb force $\frac{Q_{1}Q_{2}}{4\pi d^{2}\varepsilon_0}$
- Let $k=\frac{1}{4\pi \varepsilon_0}$ to get
$$F = \frac{k Q_{1}Q_{2}}{d^{2}}$$
Completed
## Chapter 2-Gauss Golden Cudgel
- Assuming that a uniformly charged length is positively infinitely thin and the charge density is $\lambda$, find the field strength $d$ away from it.
- Draw a cylinder around the rod and set the height to be $x$.
- Due to the infinite length of the rod, the electric fields on the two bottom surfaces of the cylinder are cancelled.
- The cylindrical side area is $2\pi dx$
- The amount of charge in the cylinder is $\lambda x$
- Introduce Gaussian, get
$$
2\pi dxE = \frac{\lambda x}{\varepsilon_{0}}
$$
Organized
$$
E = \frac{\lambda}{2\pi d\varepsilon_{0}}
$$
Completed
## Gauss Ball Ball
- First, there must be a charged ball with electricity $Q$, and I want to find the field strength at the distance of $d$ from the center of the ball.
- Then columnable
$$
4\pi d^2 E = \frac{Q}{\varepsilon_0}
$$
Organized
$$
E = \frac{Q}{4\pi \varepsilon_0 d^2}
$$
complete
## Gaussian Noodles
- First, there is a uniformly charged infinite surface, the charged surface density is $\rho$, and the field strength of the point $d$ is desired.
- Using the infinite plane as the central cross section, make a cylinder with the center of the bottom surface as the point to be found, and the radius is $r$.
- Since the electric field lines are all parallel, only two bottom surfaces have electric field lines passing through.