Consider the following image: A proton enters a magnetic field at right angles to it, as shown above. The direction of force acting on the proton will be

Correct — D, into the page. The printed figure shows a single arrow pointing straight up the page labelled 'Proton', crossed by a set of parallel arrows pointing to the right labelled 'Magnetic field'. Both directions therefore lie in the plane of the page, at right angles to each other, exactly as the stem says.

The magnetic force on a moving charge is F = q(v × B). A proton carries positive charge, so F points along v × B itself, with no reversal.

Apply the right-hand rule to v × B: point the fingers along v (up the page), curl them towards B (to the right), and the thumb points into the page. Equivalently, with the usual axes — x to the right, y up, z out of the page — v is along +y and B along +x, and ŷ × x̂ = −ẑ, which is into the page.

So the force is perpendicular to both the velocity and the field, directed into the page.

Why the others are wrong

• (a)
  to the right — This is the direction of the magnetic field itself. The magnetic force is always perpendicular to B, so it can never point along the field.
• (b)
  to the left — This is simply the field direction reversed. It is still parallel to B, and the force on a moving charge is never parallel or antiparallel to the field.
• (c)
  out of the page — The right axis, wrong sense. Out of the page is what you get by taking B × v instead of v × B, or by using the left hand for a positive charge. For a proton moving up with the field to the right, the force is into the page.

A charge moving through a magnetic field feels F = q(v × B), whose magnitude is qvB sin θ and whose direction is perpendicular to the plane containing v and B. Because the force is always at right angles to the velocity, it changes the direction of motion but never the speed — which is why a charged particle in a uniform field travels in a circle rather than speeding up.

Key facts

• F = q(v × B); magnitude qvB sin θ, and qvB when v is perpendicular to B.
• The force is perpendicular to BOTH v and B, so it is never along the field.
• For a positive charge the right-hand rule gives the direction directly.
• Here v is up the page and B to the right, so v × B is into the page.
• The magnetic force does no work — it changes direction, not speed.

Common traps

• Choosing a direction parallel to the magnetic field.
• Computing B × v instead of v × B, which reverses the answer.
• Using the left hand for a positive charge, or forgetting that an electron reverses the result.
• Assuming the force speeds the particle up rather than turning it.

• practice — not a real PYQ

  An electron moves upwards in the plane of the page through a magnetic field directed to the right in the same plane. The force on the electron is

  • (a)into the page
  • (b)out of the page
  • (c)to the left
  • (d)zero
  Answer(b) out of the page — v × B is into the page, and the electron's negative charge reverses it.
• practice — not a real PYQ

  A charged particle moves parallel to a uniform magnetic field. The magnetic force on it is

  • (a)maximum
  • (b)zero
  • (c)qvB
  • (d)directed along the velocity
  Answer(b) zero — with θ = 0, sin θ = 0, so F = qvB sin θ vanishes.