Question

The magnetic force cannot do work on a charged particle since the force is always perpendicular to the velocity. How then can magnets pick up nails? Consider two parallel current-carrying wires. The magnetic fields cause attractive forces between the wires, so it appears that the magnetic field due to one wire is doing work on the other wire. How is this explained? a) The magnetic force can do no work on isolated charges; this says nothing about the work it can do on charges confined in a conductor. b) Since only an electric field can do work on charges, it is actually the electric fields doing the work here. c) This apparent work is due to another type of force.

Short answer

Based on the given information and analysis, explain why magnets can pick up nails and how attractive forces between parallel current-carrying wires are formed, even though magnetic forces cannot do work on charged particles. Magnets can pick up nails because the magnetic force acts on electrons within a conductor, creating an attractive force between the magnet and the nails. This is different from the isolated charged particles on which magnetic forces cannot do work. Attractive forces between parallel current-carrying wires are formed due to their magnetic fields interacting with each other. When two wires carry currents in the same direction, their magnetic fields reinforce each other and cause an attractive force. These forces can occur because the charges within the wires are not isolated and their movement through the conductor places them in a different situation than isolated charged particles.

Step-by-step solution

Understanding magnetic force on charged particles

Magnetic forces cannot do work on isolated charged particles because the force is always perpendicular to the velocity of the particle. This means that the particle moves in a circular path, and the magnetic force continuously changes direction to remain orthogonal to the velocity vector of the charged particle. Since no displacement occurs in the direction of the force, no work is done on the charged particle.

Statement A

Statement A suggests that magnetic forces can do no work on isolated charges, but that doesn't mean they cannot do any work on charges confined in a conductor. When a magnetic field is applied to a conductor, it causes a force on the electrons within the conductor. These electrons are not isolated and can be influenced by the magnetic field as they move through the conductor. This movement of electrons, known as current, can cause a force, allowing magnets to pick up nails.

Magnetic force on parallel current-carrying wires

When two parallel current-carrying wires generate magnetic fields, these fields can cause attractive forces between the wires. The magnetic field due to one wire can interact with the other wire and its associated charges, causing it to exert a force. This force, in turn, does work on the other wire, seemingly contradicting the principle that magnetic forces cannot do work on charged particles.

Statement B

Statement B mentions that only electric fields can do work on charges, and that electric fields are actually responsible for the observed effect. However, this statement is not entirely accurate. While it is true that electric fields can do work on charges, magnetic fields interacting with current-carrying wires can also produce forces and do work. This is due to the fact that the charges are not isolated in the wire, and their movement through the conductor places them in a different situation than isolated charged particles.

Statement C

Statement C suggests that the apparent work is due to another type of force. While this statement is not an accurate explanation in itself, it brings up the idea of considering other forces beyond magnetic and electric fields. In the case of parallel current-carrying wires, the magnetic force is indeed responsible for the attractive force between the wires. When two wires carry currents in the same direction, their magnetic fields reinforce each other and cause an attractive force. On the other hand, if the currents flow in opposite directions, they produce repulsive forces.

Conclusion

In summary, magnets can pick up nails because the magnetic force acts on electrons within a conductor, creating an attractive force between the magnet and the nails. This is different from the isolated charged particles on which magnetic forces cannot do work. Additionally, parallel current-carrying wires can experience attractive or repulsive forces due to their magnetic fields interacting with each other, even though magnetic forces cannot do work on isolated charged particles. None of the given statements (a, b, or c) fully and accurately explain the phenomena, but statement A offers the most insight into the effects of magnetic forces on confined charges within conductors.

Key concepts

Work on Charged Particles

It's a common misconception that magnetic forces can do work on charged particles. In physics, work is defined as the force acting on an object causing displacement in the direction of the force. However, when dealing with charged particles, magnetic forces are unique because they always act perpendicular to the velocity of the charged particle. This perpendicularity means that the particle may move, but not in the direction of the magnetic force. As a result, no work is actually being done on the charged particle.

For example, imagine a charged particle moving through a magnetic field. The magnetic force causes the particle to follow a circular or helical path, but since the force is at a right angle to the motion, the actual path length or the speed of the particle doesn't change due to the magnetic force alone. Thus, according to the formal definition, the magnetic force does no work on an isolated moving charge. Electricity and magnetism concepts show that other types of forces, such as electric forces, can do work on charged particles to change their velocities, not magnetic forces.

Current-Carrying Wires

When it comes to current-carrying wires, the interplay between electricity and magnetism becomes even more fascinating. Inside a wire carrying an electric current, numerous free electrons are moving. These moving charges produce magnetic fields, and that is where our understanding of forces and work shifts a bit.

Normally, magnetic fields interact with other magnetic fields or magnetic materials by exerting forces at a distance. In the intriguing scenario of two parallel current-carrying wires, each wire produces a magnetic field that affects the other. If both wires carry current in the same direction, they will attract each other, suggesting that work is being done. While this force is magnetic in nature, it ultimately influences the entire wire, which contains a vast array of charges that are not isolated but bound within the metal lattice. Hence, these inner dynamics defy the strict notion that magnetic forces cannot perform work, reshaping our understanding in the context of conductive materials.

Electric Fields

We navigate from the realm of magnetism to electric fields, which play a vital role in the force and work exerted on charged particles. Unlike magnetic fields, electric fields do have the ability to do work on charges. An electric field is essentially a region around a charged particle where a force would be experienced by other charges.

In the case of a stationary charged particle, if placed in an electric field, it would experience a force in the direction of that field. This force can cause the particle to accelerate, resulting in work being done on the particle. It's an electric field's fundamental characteristic that it can change the kinetic energy of a charged particle, contrasting with magnetic forces, which only change the direction of motion without doing work on isolated charges. This distinction is crucial in understanding the forces at play particularly when examining electromagnetic devices and the principles of electric circuits.

Magnetic Fields

Magnetic fields are as mysterious as they are pervasive in the physical world. Generated by moving electrical charges, these fields can exert forces on other moving charges and magnetic materials. The very essence of a magnetic field revolves around its influence on its surroundings, namely its ability to induce a force on a magnetic object or another magnetic field.

While we have established that these forces don't do work on charged particles, they do shape the trajectories of these particles and can cause shifts in their paths without changing their speeds. For instance, a charged particle emits a magnetic field when it moves, and in the presence of an external magnetic field, a force known as the Lorentz force acts on it, causing deflection. The beauty of magnetic fields lies in their ability to influence without imparting energy directly to charged particles, a key principle in the operation of many technological devices such as electric motors and generators.