Direction of force on positive and negative charged particles.

The idea

A charged particle moving in a magnetic field experiences a force only when its velocity has a component perpendicular to the field. The magnitude is given by F = Bqv sin θ, where θ is the angle between velocity and field; the force is zero when the particle moves parallel to the field. The direction is found from the left-hand rule for positive charges: first finger field, second finger conventional current, thumb force. For a negative particle such as an electron, the conventional current is opposite to the particle's velocity, so the force reverses compared with a positive particle moving the same way. The force is always perpendicular to velocity, so it does no work and changes direction but not speed. Example: an electron moving east through a field directed north feels a force vertically downwards, whereas a proton moving east feels a force vertically upwards.

What earns the marks

• State that the magnetic force on a moving charge has magnitude F = Bqv sin θ, where θ is the angle between velocity and magnetic field, and is zero when the particle moves parallel to the field.
• Apply the left-hand rule correctly: first finger along the magnetic field, second finger along conventional current, thumb giving the force on a positive charge.
• Explain that for a negative charge the conventional current is opposite to the velocity, so the force direction is opposite to that on a positive charge with the same velocity.
• Recognise that the force is perpendicular to velocity, so it acts as a centripetal force, changing direction but not speed or kinetic energy.
• Use a diagram or vector reasoning to determine the force direction for a given field and velocity, including cases where the velocity is at an angle to the field.
• Distinguish between the force on a stationary charge (zero) and on a moving charge, and between motion parallel and perpendicular to the field.

Common mistakes and how to put them right

• Treating the second finger of the left-hand rule as the direction of motion of a negative particle.

  Put it right: Point the second finger along conventional current, which is opposite to the electron's velocity.

• Assuming the magnetic force can change the speed of a charged particle.

  Put it right: The force is always perpendicular to velocity, so it does no work and only changes direction.

• Using the right-hand rule for a moving charge.

  Put it right: Use the left-hand rule for the force on a positive charge and then reverse the result for a negative charge.

• Treating F = Bqv sin θ as giving the direction of the force.

  Put it right: This equation gives only the magnitude, and the direction must be found from the left-hand rule or the vector product.

Exam tips

• Sketch the field, velocity and force vectors before substituting numbers, so the direction is clear and can be checked against the left-hand rule.
• When the charge is negative, state explicitly that the conventional current is opposite to the velocity before giving the force direction.
• Check whether the velocity is parallel to the field: if it is, the magnetic force is zero and no deflection occurs.