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 or attraction force between two current-carrying conductors or a force experienced by a charged particle moving through a magnetic field and is determined by the formulas below
\begin{align*} \vec{F}_B&=i\vec{\ell}\times \vec{B} \\ \vec{F}_B&=q\vec{v}\times \vec{B} \end{align*} where $\times$ is the cross product of the two vectors.
In short: an electric force is completely independent of velocity but the magnetic force is essentially dependent on velocity.
Direction of Forces:
The direction of the electric force between two charges is along the joining line of them (Figure below) but that of magnetic force is always perpendicular to the plane of $\vec{v}\, -\, \vec{B}$ and is determined by the right-hand rule.
- The source of the creation of electric force is charged objects or particles which arise in the so-called two kinds called positive and negative.
- Electric force does work on a rest or moving charge BUT the magnetic force does only work on moving charge.
- The electric force vector is along the direction of the electric field $\vec E$, BUT the magnetic force is perpendicular to the plane of $\vec v-\vec B$.
- Electric force can change the speed or kinetic energy of a particle BUT magnetic force can alter only the direction of the velocity of a particle.
You can also learn the difference between transverse and longitudinal waves quickly.
Electric force and magnetic force absolutely solved problems.
kinematic
Electrostatic
Magnetism