If a magnetic field is applied parallel to a charge moving in a straight line, the direction of the charge will be:

The correct answer is rectilinear.

Key Points

• If a magnetic field is applied parallel to the motion of a charged particle, it does not exert any force on the particle as the velocity vector and magnetic field vector are parallel.
• The force exerted by a magnetic field on a moving charge is given by the formula F = q(v × B), where q is the charge, v is the velocity, and B is the magnetic field. If v and B are parallel, the cross product is zero, hence no force is applied.
• In the absence of any perpendicular force, the charged particle continues to move in a rectilinear path (straight line).
• This phenomenon aligns with the principles of classical electromagnetism described by Lorentz force law.
• Charged particles deviate from rectilinear motion only when the magnetic field is applied at an angle other than parallel to their velocity.

Additional Information

• Magnetic Force: The force exerted by a magnetic field on a moving charge depends on the orientation of the field relative to the charge's velocity.
• Lorentz Force Law: It states that the force on a charged particle is a combination of electric and magnetic forces, given by F = q(E + v × B).
• Cross Product in Physics: In vector mathematics, the cross product determines the perpendicular component of the interaction between two vectors. When vectors are parallel, the cross product is zero.
• Types of Motion in Magnetic Fields: Charged particles exhibit different trajectories such as circular, spiral, or elliptical motion when the magnetic field is applied at angles other than parallel.
• Applications: Understanding the motion of charges in magnetic fields is crucial for devices like cyclotrons, mass spectrometers, and the study of plasma physics.