diff --git a/docs/sph4u7.md b/docs/sph4u7.md index 1ef3d39..6ed3776 100644 --- a/docs/sph4u7.md +++ b/docs/sph4u7.md @@ -43,6 +43,34 @@ The right-hand rule can be applied again to a selenoid to identify the direction (Source: Kognity) +### Properties of moving charges + +As only moving electric charges generate magnetic fields, stationary electric charges are **unaffected** by external magnetic fields. Moving charges are affected by Newton's third law of motion — equal and opposite forces are exerted on the charge and the magnet. As such, where $q$ is the charge of the particle and $\vec{v}\times \vec{B}$ is the **cross product** (vector multiplication) of the velocity of the particle and the magnetic field strength in Teslas: +$$\vec{F_m}=q\vec{v}\times \vec{B}$$ + +**Magnetic field strength** ($B$) represents the force acting per unit current in a conductor of unit length perpendicular to the field with the unit Tesla ($\pu{T}$) + +The **magnetic force** is always plane **perpendicular** to both $\vec{v}$ and $\vec{B}$. Just the magnitude of the force can be found by using the angle between the two vectors ($\theta$): +$$|F_m|=qvB\sin\theta$$ + +Regardless of $\theta$, the force vector is always perpendicular to both $B$ and $v$, + +The above equation can be rearranged to find **electromagnetic** force in terms of current and wire length in a **uniform magnetic field**: +$$|F_em|=BIL\sin\theta$$ + +(Source: Kognity + +The **right-hand-rule** can be used to determine the direction of force — the thumb points in the direction of current/velocity, the fingers point in the direction of the magnetic field, and the palm points in the direction of force. Alternatively, just three fingers can be used. + +(Source: Kognity) + +When two straight-line conductors with current flowing through them are brought together, they either mutually attract or repel. The ampere is defined based on the current required to flow through a scenario involving two parallel straight-line conductors. + +(Source: Kognity) + +Inside a **uniform magnetic field**, charges move in **uniform circular motion** at a constant velocity. If the particle did not enter the field at a perfect right angle, some of the velocity is used to change the path of the particle to be in a spiral — still perfectly circular, but additionally moving in the third dimension perpendicular to the circle. +$$\Sigma F_c = F_m$$ + ## Resources - [IB Physics Data Booklet](/resources/g11/ib-physics-data-booklet.pdf)