If a magnetic field is applied perpendicular to the velocity of a charge moving in a straight line, the trajectory of the charge will be:

The Correct answer is circular.

Key Points

• When a magnetic field is applied perpendicular to the velocity of a charged particle, it experiences a force called the Lorentz Force.
• The direction of the Lorentz Force is determined by the right-hand rule and is always perpendicular to both the velocity and the magnetic field.
• Because the force is perpendicular to the velocity, the charged particle undergoes uniform circular motion.
• The radius of the circular trajectory depends on factors such as the charge of the particle, its velocity, the strength of the magnetic field, and the mass of the particle.
• The formula for the radius of the circular motion is r = mv / (qB), where m is the mass, v is the velocity, q is the charge, and B is the magnetic field strength.
• This phenomenon is widely applied in devices like cyclotrons and mass spectrometers, which rely on the circular motion of charged particles in a magnetic field.

 Additional Information

• Linear
  • When the velocity of a charged particle is parallel or anti-parallel to the magnetic field, there is no force acting on the particle, and its motion remains linear.
  • This is due to the equation of Lorentz Force, where F = q(v x B). If v and B are parallel, the cross-product results in zero force.
• Spiral
  • A charged particle moves in a spiral trajectory if it has both parallel and perpendicular components of velocity with respect to the magnetic field.
  • The parallel component allows the particle to move along the field lines, while the perpendicular component causes circular motion, resulting in a spiral path.
• Elliptical
  • An elliptical trajectory occurs under specific conditions, such as the presence of multiple forces acting on the particle or variations in the magnetic field strength.
  • It is less common compared to circular or spiral motion in uniform magnetic fields.