What will happen if a collection of positive and negative charges are passed at a high speed through a magnetic field which is perpendicular to the direction of motion of the charges ? (Assume that both kind of charges are NOT going to recombine)
- (a)Both kind of charges will stop moving
- (b)Positive charges and negative charges will separate out
- (c)Positive charges will stop but negative charges will continue moving uninterrupted
- (d)Both kind of charges will keep moving uninterrupted
Correct — B, Positive charges and negative charges will separate out. A charge moving in a magnetic field feels the force F = qv × B. With the velocity perpendicular to the field the magnitude is qvB, the largest it can be, and the direction is at right angles to both v and B. Reverse the sign of the charge and that direction reverses. So a positive charge is pushed one way and a negative charge, moving alongside it at the same speed, is pushed the opposite way — the mixed stream splits into two beams that curve apart.
- (a)Both kind of charges will stop moving — The magnetic force is always perpendicular to the velocity, so it does no work on the charge. It can bend the path but cannot change the speed, and it can never bring a charge to rest.
- (c)Positive charges will stop but negative charges will continue moving uninterrupted — This gets the asymmetry backwards. Both signs feel a force of the same magnitude qvB for the same speed and charge size; what differs is only the direction. And neither can be stopped, for the same no-work reason.
- (d)Both kind of charges will keep moving uninterrupted — This would be true only if the velocity were parallel or antiparallel to the field, when v × B vanishes and no force acts. The stem states the field is perpendicular to the motion, which is exactly the case that gives the maximum force.
The magnetic force on a moving charge is F = qv × B. Three consequences follow and they answer most NDA questions on the topic. Its magnitude is qvB sin θ, so it is greatest when the velocity is perpendicular to the field and zero when the two are along the same line. Its direction depends on the sign of q, so opposite charges are deflected opposite ways. And because it is always perpendicular to the velocity it does no work, so the speed and the kinetic energy are unchanged — a perpendicular field bends a charge into a circular arc rather than speeding it up or slowing it down.
The question describes the working principle of a charge separator, and the same physics runs the mass spectrometer and the velocity selector, where a magnetic field sorts a beam by charge and by mass. On the largest scale it is why the Earth's magnetosphere deflects the charged particles of the solar wind and funnels them toward the poles instead of letting them reach the ground. The parenthetical instruction not to let the charges recombine is the examiner closing off a chemistry answer: without it a student might argue the separated species simply re-attract, which is not what the physics of the deflection itself predicts.
- The magnetic force on a moving charge is F = qv × B, of magnitude qvB sin θ.
- It is maximum when the velocity is perpendicular to the field and zero when the velocity is along the field.
- Because the force is perpendicular to the velocity it does no work, so the speed cannot change.
- Reversing the sign of the charge reverses the direction of the force, which is why opposite charges separate.
- Assuming a magnetic field can speed up or stop a charge — it cannot, because the force does no work.
- Forgetting the sin θ factor, and so missing that a charge moving along the field line feels no force at all.
- Thinking the force is larger on the positive charge; for equal charge magnitude and speed the two forces are equal and opposite in direction.
Asked as a qualitative 'what happens to the charge' item like this, or as a direction question where you must apply the cross product to a stated field and velocity.
Electrically charged particles from space travelling at speeds of several hundred km/sec can severely harm living beings if they reach the surface of the Earth. What prevents them from reaching the surface of the Earth ?
- (a) The Earth's magnetic field diverts them towards its poles
- (b) Ozone layer around the Earth reflects them back to outer space
- (c) Moisture in the upper layers of atmosphere prevents them from reaching the surface of the Earth
- (d) None of the statements (a), (b) and (c) given above is correct
Answer(a) The Earth's magnetic field diverts them towards its poles
The same force at planetary scale. Fast charges meeting a magnetic field are deflected rather than stopped, and the Earth's field steers them along its lines toward the poles — the reason aurorae are a polar phenomenon.
A positive charge is moving towards south in a space where magnetic field is pointing in the north direction. The moving charge will experience :
- (a) a deflecting force towards north direction.
- (b) a deflecting force towards east direction.
- (c) a deflecting force towards west direction.
- (d) no deflecting force.
Answer(d) no deflecting force.
The complementary case, set six months earlier in the same exam year. There the velocity was along the field line, so the force vanished; here it is perpendicular, so the force is at its maximum. The two together define the sin θ factor.
- practice — not a real PYQ
A charged particle moves through a uniform magnetic field. Which one of the following quantities of the particle remains unchanged?
- (a)Direction of velocity
- (b)Speed
- (c)Momentum
- (d)Direction of acceleration
Answer(b) Speed — the magnetic force is perpendicular to the velocity and therefore does no work.
- practice — not a real PYQ
An electron enters a uniform magnetic field with its velocity parallel to the field lines. The force experienced by the electron is
- (a)maximum, equal to qvB
- (b)zero
- (c)qvB directed along the field
- (d)qvB directed opposite to the field
Answer(b) zero — with the velocity along the field, sin θ is zero and v × B vanishes.