Problem 56 STATEMENT-1 : A neutral conducti... [FREE SOLUTION] (2024)

Short Answer

Lorentz force law

The Lorentz force law is a fundamental principle in electromagnetism. It describes the force experienced by a charged particle due to electric and magnetic fields. The law is formulated as \(\textbf{F} = q(\textbf{E} + \textbf{v} \times \textbf{B})\), where \(\textbf{F}\) is the force on the charge, \(q\) is the electric charge, \(\textbf{E}\) is the electric field, \(\textbf{v}\) is the velocity of the charge, and \(\textbf{B}\) is the magnetic field.

Neutral conducting wire

A neutral conducting wire means that, overall, the wire has no net electric charge. However, it still contains electrons and ions within. It's important to understand that without the movement of these charges (i.e., no current), the magnetic field does not exert a force on the wire.
This is because, according to the Lorentz force law, the magnetic force arises due to the motion of charges. If the charges aren't moving, the force is zero. This explains why a neutral conducting wire under a uniform magnetic field experiences no net magnetic force.

Uniform magnetic field

A uniform magnetic field is one where the magnetic field strength and direction are constant throughout a specified region. This means that the field lines are parallel and equally spaced. When a conducting wire with no current is placed in such a field, the charges within the wire are stationary. The uniform magnetic field doesn't affect stationary charges as the Lorentz force law relies on the motion of these charges to exert a force.
Thus, the neutral wire remains unaffected by the uniform magnetic field if there is no current flowing through it.

Current and magnetic force

Current refers to the flow of electric charges, typically through a conductor like a wire. When there is a current, charges within the conductor are moving. According to the Lorentz force law, these moving charges will experience a magnetic force in the presence of a magnetic field. The direction and magnitude of this force depend on the velocity of the charges and the orientation of the magnetic field.
Specifically, the force is perpendicular to both the direction of the magnetic field and the velocity of the moving charges. This is why, in the absence of current, no magnetic force is exerted on the wire or the electrons within it.