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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 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 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.