Consider a wire carrying a steady current, I placed in a...

Consider a wire carrying a steady current, $I$ placed in a uniform magnetic field $\mathbf{B}$ perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do no work. This implies that, $\quad$ [NCERT Exemplar] (a) motion of charges inside the conductor is unaffected by B since they do not absorb energy (b) some charges inside the wire move to the surface as a result of B (c) if the wire moves under the influence of $\mathrm{B}$, no work is done by the force (d) if the wire moves under the influence of $\mathrm{B}$, no work is done by the magnetic force on the ions, assumed fixed within the wire

Consider a wire carrying a steady current, $I$ placed in a uniform magnetic field $\mathbf{B}$ perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do no work. This implies that, $\quad$ [NCERT Exemplar]
(a) motion of charges inside the conductor is unaffected by B since they do not absorb energy
(b) some charges inside the wire move to the surface as a result of B
(c) if the wire moves under the influence of $\mathrm{B}$, no work is done by the force
(d) if the wire moves under the influence of $\mathrm{B}$, no work is done by the magnetic force on the ions, assumed fixed within the wire

Key Concepts

Lorentz Force Law

The Lorentz force law states that a moving charge in a magnetic field experiences a force perpendicular to both its velocity and the magnetic field. This is expressed mathematically as F = q(v × B). Because the magnetic force is always perpendicular to the direction of motion, it does not change the kinetic energy of the charge, implying that the magnetic field does no work on the charge directly.

Magnetic Forces and Work

A key concept in electromagnetism is that magnetic forces do no work on moving charges because the work done is determined by the component of force along the direction of displacement. Since the force from a magnetic field is always perpendicular to the displacement of the charge, the dot product F · d does not yield energy transfer, meaning that while the magnetic force can change the direction of the particle’s motion, it cannot alter its speed or kinetic energy.

Current-Carrying Conductor in a Magnetic Field

When a conductor carrying an electric current is placed in a magnetic field, the individual moving charges inside the conductor experience magnetic forces according to the Lorentz force law. Although these forces act on the charges, the net work done by the magnetic field on these charges remains zero because each force acts perpendicular to the instantaneous velocity of the charge. However, a net force on the conductor can be observed macroscopically due to the collective effect of these forces, and any work done on the conductor as a whole is accounted for by energy supplied by the power source, not by the magnetic field.

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