Motion in the Presence of Electric and Magnetic Field

We go for a walk early in the morning.

Because it would be difficult to walk in the afternoon due to the Sun’s heat.

Similarly, the motion of charges is also affected by the electric and magnetic fields.

Now let’s understand the motion in the presence of only Magnetic Field.

The force exerted on a particle moving through both the Electric and Magnetic field is known as Lorentz Force.

It is given by, $F=qE+qv\times B$ Where, $q=$ charge on the particle $v=$ velocity of the particle $E=$ Electric Field $B=$ Magnetic Field

When there is only Magnetic Field and no Electric Field, the particle traces a circular path.

The radius of the circle is given by, $r=\frac{mv}{qB}$ where m = mass of the particle

In this case, the velocity of the particle v is perpendicular to the direction of Magnetic field B.

Now let’s study the motion of the particle in the presence of Electric and Magnetic field.

The Electric Field can deflect the trajectory of the charged particle.

If the Electric field and Magnetic field are equal and opposite in direction, then no force acts on the particle.

$\therefore F=qE+qv\times B$ $\therefore 0=qE+qv\times B$ $\therefore E=v\times B$ $\therefore v=\frac{E}{B}$

Therefore, the velocity of the particle v, Electric Field E and magnetic field B are perpendicular to each other.

When velocity becomes parallel to Electric Field, the particle follows a helical path.

If the Electric Field is along the Y-axis then the particle moves in helical motion along the same axis.

Revision

When a particle is in motion in the presence of Electric Field and Magnetic Field, Lorentz force acts on it.

Lorentz force is given by, $F=qE+qv\times B$

The End