# Flash Cards

Magnetism

## Motion of a charged particle in a uniform magnetic field

When the velocity of a charged particle $\vec v$ is perpendicular to a uniform $\vec B$, the particle moves around a circle in a plane perpendicular to $\vec B$.  There is always a centripetal force in a circular path, which in this case provided by magnetic force, therefore the radius of the circular path is  $\underbrace{qvB}_{F_B}=\frac{mv^{2}}{r} \quad \Rightarrow \quad r=\frac{mv}{qB}$ The time required to particle travel one circle or the period of motion is the circumference of the circle divided by the velocity of charged particle $T=\frac{2πr}{v}=\frac{2πm}{qB}$ The angular speed of the particle $\omega$, which is called cyclotron frequency, is

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Electrostatic

## Relation between electric force and electric field

To find the electric field at each point in vicinity of a charged particle $q$, place a small and insignificant positive charge, called test charge, $q_0$ at that point and then measure the force $\vec{F}$acting on it. The electric field $\overrightarrow{E}$ due to that point charge $q$ is defined as  $\vec{E}=\frac{\vec{F}}{q_0}$  Electric field is a vector quantity that its magnitude is $E=F/q_0$ and its direction is in the same direction as the force acting on the test charge. In the other words, electric field points in opposite direction of the electric force acting on a negative charged particle.

Magnetism

## Charged particle in magnetic field

If a particle of charge q and velocity $\vec v$ enters a region of space occupied by magnetic field $\vec B$, which is establishes by some source, it experiences a magnetic force $\vec F_B$ given by  $\vec F_B=q\vec v \times \vec B$ Using definition of the cross product, we obtain its magnitude as $|\vec F_B|=|q|vB\, \sin \theta$ Where $\theta$ is the smaller angle between $\vec v$ and $\vec B$.

Magnetism

## The direction of the magnetic force on a positive charge

Version 1 (right hand rule): point fingers of your right hand in the direction of $\vec v$ and curl them (through the smaller angle) toward $\vec B$. Your upright thumb shows the cross product $\vec v \times \vec B$ or the magnetic force $\vec F_B$. This force is perpendicular to the plane of $\vec v-\vec B$ Version 2 (right hand rule): point your fingers in the direction of $\vec B$ so the thumb points toward the velocity $\vec v$, the magnetic force on a positive charge is in the outward direction of your palm. Note: the magnetic force on a negative charge is in opposite direction to that given right hand rule.

Magnetism

## Properties of magnetic force

(1) The magnitude of a magnetic force depends only on the magnitude of the charge i.e. $F\propto |q|$ (2)  Magnetic force is always perpendicular to the plane containing $\vec v$ and $\vec B$. (3)  A charge moving parallel $\theta=0$ to a magnetic field experiences zero magnetic force.  (4)  A charge moving perpendicular $\theta =90{}^\circ$ to a magnetic field experiences a maximum magnetic force $F_B=qvB$. (5)  The magnetic force on a positively charge particle is in opposite direction to that of a negatively charge particle i.e. $\vec F_{B(q)}=\vec F_{B(-q)}$

kinemtic

Electrostatic

## Superposition principle

The net electric field or force of a group of point charges at each point in space is the vector sum of the electric fields due to the individual charges at that point. in the mathematical form is written as  ${\vec{E}}_{net}={\vec{E}}_1+{\vec{E}}_2+\dots +{\vec{E}}_n$