Earth Defense Force An alien civilization has crossed the galaxy to invade the E

Question

Earth Defense Force

An alien civilization has crossed the galaxy to invade the Earth and enslave humanity, again. Their attacks have been successful so far because their assault troops are equipped with handheld weapons that project beams of charged particles (protons & electrons) at very high speeds, able to melt or vaporize solid objects on contact. To counter this frightening weapon, the Earth Defense Force has developed a super-strength bar magnet that can be attached to a human soldier's helmet or weapon, so that its magnetic field will stop or deflect the charged particles.

Question: in order for the magnet to counter a beam being fired at a soldier from directly in front, how should the bar magnet be oriented? Should the N or the S pole be pointing directly forward? Or should it be vertical, and if so, should the N or the S pole point upward? Or won't this work at all? Explain your reasoning.

Explanation / Answer

Force acting on a charged particle moving in a magnetic field:
                         Force, F = q v B sin

Here,
q = Charge of the particle
v = Velocity of the charged particle
B = Strength of the magnetic field
= Angle between velocity of the charged particle and magnetic field

It is given that the beam is fired directly in front of the soldier i.e in horizontal
direction.

Case I: ( Magnet in horizontal position)
If the magnet is also kept in horizontal direction, then the angle between beam
of charged particles and magnetic field is either 00 or 1800.
Force on charge particle, F = q v B sin 00 (or) q v B sin 1800
                                          = 0
As the force acting on the charged particles is equal to zero, the charged
particles cannot deflect. So, this method cannot work.

Case II: ( Magnet in vertical position)
If the magnet is kept in vertical direction, then the angle between beam
of charged particles and magnetic field is either 900 or 2700.
Force on charge particle, F = q v B sin 900 (or) q v B sin 2700
                                          = ± q v B
As the force acting on the charged particles is non-zero, the charged
particles deflects either left or right. In this case, the direction of deflection
of protons and electrons is opposite.

Hence, the magnet should kept in vertical direction with either
N pole or S pole kept upward.

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