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# System prepended metadata

title: Physics II - B14

---

# Physics II - B14
## Magnetic Force Between Two Parallel Conductors
<center><img src = "https://i.imgur.com/Y3D20PF.png" width = 350 height = 250></center>

$$
\vec F_1 = I_1\vec l \times \vec B_2
$$

$$
\to F_1 = I_1lB
$$

$$
B_2 = \frac{\mu_0I_2}{2\pi a}
$$

$$
\frac{F_1}{l} = \frac{\mu_0I_1I_2}{2\pi a}
= \frac {2\times10^{-7} (N)}{1(m)} = \frac{\mu_0 (1A)^2}{2\pi (1m)}
$$
$\Rightarrow$ **the definition of Ampere**

**<span style="color: red">Parallel conductors carrying currents in the same direction attract each other, and parallel conductors carrying currents in opposite directions repel each other.</span>**

## Magnetic Field for a Long, Straight Conductor
![](https://i.imgur.com/3HDyJ02.png)

## Magnetic Field for a Circular Current Loop
![](https://i.imgur.com/xOmLG1H.png)

## Magnetic Field Lines for a Loop
![](https://i.imgur.com/wNJijCZ.png)

## Ampere’s Law
![](https://i.imgur.com/wWgqfCN.png)

## Long Wire with Finite Thickness
![](https://i.imgur.com/stZ6Lzq.png)

## Magnetic Field of a Toroid
![](https://i.imgur.com/ZHk0nZG.png)

## Magnetic Field of a Solenoid
* **The magnetic field lines resemble that of a magnet.**
<img src = "https://i.imgur.com/PR8TvQ3.png" width = 300 height = 450>

* **Uniform field:** parallel and equally spaced
<img src = "https://i.imgur.com/JO7vIi9.png" width = 300 height = 450>

<center><img src = "https://i.imgur.com/xbG814G.png" width = 600 height = 150></center>


