# Flash Cards

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 the 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:

Magnetism

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

The direction of the magnetic force on a moving positively charged particle or a wire carrying current $i$ in a uniform magnetic field 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 direct

kinematic

## Acceleration on Position-Time Graph

Acceleration on a position vs. time graph can be obtained, by having the initial position and velocity of a moving object. In this article, we want to show you how to find constant acceleration from a position-time graph with some solved problems. You can skip this introduction and refer to problems 6 and 7.  Types of Motion: An object can move at a constant speed or have a changing velocity. Suppose you are driving a car at a constant speed of $100\,{\rm km/h}$ along a straight line. What does mean by $100\,{\rm km/h}$?  The speed of $100\,{\rm km/h}$ indicates that you drive the first 100 km in the first hour, the next 100 km during the second hour, an

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 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 that 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 are $|q|$ and $|q'|$. But magnetic force is a repulsion

kinematic

## Displacement and distance problems with solutions

Problems and Solutions about distance and displacement are presented and updated useful for high school and college students. In the following, displacement is computed for simple cases, 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 point A, its initial position. Now, Find the displacement and distance?   Solution (1): (a) By definition of displacement, connect the initial (A) and final (D) points together. As shown, displacement is toward the n

kinematic

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