 # Flash Cards

Magnetism

## Helical Path: Charges in Magnetic Field with Solved Example

Helical path is the path of the motion of a charged particle when enters at an angle of $\theta$ in a uniform magnetic field $B$. In this short tutorial, we explain the factors that cause this type of motion. On a moving charged particle in a uniform magnetic field, a magnetic force of magnitude $F_B=qv\,B\,\sin \theta$ is acted where $\theta$ is the angle of velocity $\vec{v}$ with the magnetic field $\vec{B}$. This is the main factor that creates a spiral or helical path.  A charged particle (say, electron) can enter a region filled with uniform $B$ either with right angle $\theta=90^\circ$ or at angle $\theta$. In the former case, its path results in a circular path, and in the

Magnetism

## Direction of Magnetic Force on a Positive Charge: Right Hand Rule

The direction of the magnetic force on a moving positively charged particle is determined by the right hand rules with different versions stated below.  Version 1 (right hand rule): point the 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 that the thumb points toward the velocity $\vec v$, your palm shows the direction of the magnetic force on a positive charge. Note: the mag

Magnetism

## Difference between electric and magnetic forces

The comparison between electric and magnetic forces in physics for high school students is presented briefly.  Definition and formulas: Electric force is repulsion or attraction between two charged objects or particles, moving or at rest, and is calculated by the Coulomb’s law with the following formula  $\vec{F}_E =k\,\frac{|q|\,|q^{'}|}{r^{2}}\,\hat{r}$ where $\hat{r}$ is the unit vector indicates the direction of the electric force and $r$ is the distance between the two charges. According to Coulomb's law, this force is proportional to the product of the magnitudes of the charges that is $|q|$ and $|q'|$. But magnetic force is a repulsion or att

kinematic

## Displacement and distance problems with solutions

Problems and Solutions about distance and displacement are presented and updated useful for highschool and college students. Problem 1:  An object moves from point A to B, C, and D finally, along a rectangle.  (a) Find the magnitude and direction of the displacement vector of the object? (b) Find the distance traveled by that object? (c) Suppose the object returns to the point A, its initial position. Now, Find the displacement and distance?   Solution to problem 1: (a) By definition of displacement, connect the initial (A) and final (D) points together. As shown, displacement is toward the negative of the y-axis and its magnitude is equal to th

kinematic

## Formula for Projectile Motion with Examples for High Schools

Definition of projectile motion: Any object that is thrown into the air with an angle $\theta$ is projectile and its motion called projectile motion. In other words, any motion in two dimensions and only under the effect of gravitational force is called projectile motion.  Formula for Projectile Motion: The following are the complete projectile motion equations in vertical and horizontal directions. In horizontal direction: \begin{align*} \text{Displacement}&:\,\Delta x=\underbrace{\left(v_0 \cos \theta\right)}_{v_{0x}}t\\ \text{Velocity}&:\, v_x=v_0 \cos \theta \end{align*} In vertical direction: \begin{align*} \text{Displacement}&:\, \Delta y=\frac 12

Electrostatic

## Electric force between charged particles

According to Coulomb's law, the magnitude of attractive or repulsive electric force between two charged particles $q_1$ and $q_2$ is proportional to the product of the magnitude of charges and inversely proportional to the distance squared $r^2$ from each other and is founded by following formula $F=k\frac{\left|q_1q_2\right|}{r^2}$  Or in vector form as $\vec{F}=k\frac{\left|q_1q_2\right|}{r^2}\hat{r}$ Where $\hat{r}$ is the unit vector along the line joining the particles to one another. In SI units, $F\to \mathrm{N}$ , $r\to \mathrm{m}$, $q\to \mathrm{C}$ and $k=9\times {10}^9\ \mathrm{N.}{\mathrm{m}}^{\mathrm{2}}\mathrm{/}{\mathrm{C}}^{\mathrm{2}}$ Note 1: the

Electrostatic

## Electric field of a point charged particle

At distance $r$ from a charged particle $q$ the magnitude of the electric field is given by the following formula $E=\frac{1}{4\pi {\epsilon }_0}\frac{\left|q\right|}{r^2}$  Note 1: the strength of the electric field around the charge $q$ is directly proportional to the magnitude of charge $|q|$ and inversely proportional with the square of distance $r$ from it.   Note 2: the electric field lines point away from positive charge and toward the negative charges.

Magnetism

## Magnetic field Lines

The space around a magnet where the forces of attraction or repulsion on a magnetic object can be detected is called magnetic field.  Magnetic field around a magnet or other magnetic object is visualized by magnetic field lines. Magnetic field around a magnet or other magnetic object can be displayed by iron filling patterns.  Magnetic field around a magnet or other magnetic object can be detected by a little compass needle at that point.  Small compass needle is aligned parallel to the magnetic field, with the north pole of the compass shows the direction of the magnetic field at that point.  The direction of magnetic field is from the north pole to the sout

Magnetism

## Drawing the field lines

To draw the magnetic field lines around a magnet or other magnetic objects, one can use the alignment of compass needle near those. The direction of these lines, in a magnet outside it, is away from N pole toward the S pole. Using small iron filing one can display magnetic field patterns around magnetic objects. The compass needles using its alignment with the magnetic field find shows the direction of the magnetic fields.

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

## 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. $\vec F_{B(q)}=\vec F_{B(-q)}$

kinematic

## kinematic parameters

Average velocity: is defined as the displacement vector divided by the total time elapsed from start to finish or in math language is defined by formula: $v_{av-x}=\frac{\Delta x}{\Delta t}=\frac{x_f-x_i}{t_f-t_i}$ Instantaneous velocity: is the limit of the average velocity as $\Delta t$ approaches zero. In one dimension, say $x$, is defined by formula $v_x=\lim_{\Delta t\to 0} \frac{\Delta x}{\Delta t}=\frac{dx}{dt}$ Instantaneous acceleration: is the limit of the average acceleration as $\Delta t$ approaches zero. In one dimension, say $x$, is defined by the followin formula $a_x=\lim_{\Delta t\to 0}\frac{\Delta v_x}{\Delta t}=\frac{dv_x}{dt}=\frac{d^2 x}{dt^2}$ \$d^{2}x/dt^2

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  ${\vec{E}}_{net}={\vec{E}}_1+{\vec{E}}_2+\dots +{\vec{E}}_n$