# The Mystery of Aurora

In 1621, a French scientist, Gassendi, saw the lights in polar regions like Alaska and Northern Canada and named after the Roman goddess of dawn, “Aurora“. He added the word “borealis” for the Roman god of the north wind, “Boreas“. In the southern hemisphere, they are called Aurora australis. The lights are usually seen after dusk near both poles. Although they look elegant and calm, aurorae are produced when a large number of charged particles undergo collision while being trapped in Earth’s magnetic field.

This splendid display of colours and appearance of dancing lights is fascinating, and equally puzzling. These haunting lights are a form of intense space weather, a result of the atmosphere shielding the Earth against fierce solar particles that would otherwise make our planet uninhabitable. Millions and millions of electrically charged particles in the solar wind wash over Earth and smash into upper atmospheric gases. The energy from each collision is released as photons – particles of light. This causes the particles to glow.

Let a charged particle of mass m and positive charge q (if the charge is negative, the direction of force shall be opposite) enter a region of uniform magnetic field B⃗ with an uniform velocity v⃗.  We shall assume that the velocity vector at this point makes an angle θ with the magnetic field vector. Let us split this vector v⃗  into its rectangular components v sin θ and v cos θ. We have to discuss a few properties of moving charges in a magnetic field at this point. The things to note here are that stationary charges experience no force in a magnetic field (Why?). Also, charges moving either parallely or anti-parallely to the direction of B⃗, experience no force (Why?). The expression for the magnetic force experienced by a charged particle is given by F⃗magnetic= q • ( v⃗  x B⃗  ). From this expression we can derive the following conclusions:

1. The force depends on the magnitudes of charge, velocity and magnetic field intensity.
2. Only charged particles can experience a magnetic force as when the charge shall be zero, the expression for force will tend to become zero.
3. The magnetic force includes a vector product ( v⃗  x B⃗  ). This can make magnetic force on that particle to be zero, if the velocity and magnetic field vectors are parallel or anti-parallel ( because A⃗  x B⃗  = |A||B| sin θ and sin θ becomes 0 when θ takes the value of 0° or 180° (in degrees), or 0 or π (in radians) ).
4. The force is zero when the charge is not moving as |v⃗ | = 0. Thus, only a moving charge experiences a force.

Now we shall pay heed to our case, we took a moving charged particle and made it enter an uniform magnetic field. The component of velocity in the direction of the field shall provide no force to the particle as θ = 0°. Hence, the component perpendicular to the field vector provides a force perpendicularly inwards (or outwards if the charge is negative).

An interesting result is that if the instantaneous displacement is in the direction of instantaneous velocity, the force is along the plane when the displacement shall be perpendicular to the plane. You should really check out the properties of vectors, if you find this hard to comprehend. This can be visualized using Right Hand Thumb Rule in which we curl our fingers from the vector A to vector B (if it is A⃗ x B⃗ ) or from vector B to vector A ( if it is B⃗ x A⃗) The thumb shall point in the direction of the vector product, which in this case, shall provide the direction of force either into the plane or out of the plane.

In an uniform circular motion, the instantaneous velocity is perpendicular to the centripetal force (force towards the center). In this case too, the instantaneous velocity is perpendicular to the force. We can thus conclude, that the component perpendicular to the field vector v sin θ has caused the particle to undergo uniform circular motion. The v cos θ component provides translatory motion (if the velocity is perpendicular to the field, then it would have no component parallel to the field and the particle shall show circular motion), so the charged particle undergoes helical motion. Even if the field bends, the helically moving particle is trapped and guided to move along the field. Since the force is normal to the velocity at each point, the field does no work on the particle and thus, the magnitude of the velocity does not change.

During a solar flare, a large number of electrons and protons are ejected from the sun. Some of them get trapped in the earth’s magnetic field and move in helical paths (as discussed) along the magnetic field. The magnetic field strength increases near the magnetic poles of the planet. Hence the density of charges increases near the poles. These particles collide with atoms and molecules of the atmosphere. The electrons in the charged atoms get excited (Zeeman effect) and move from the stable ground state to an unstable excited state. While returning back to the ground state, they emit energy in form of photons.