Question

The force needed to pull a wire along conducting rails in a magnetic field is proportional to

Answer 1

The force to pull a wire in a magnetic field depends on the current, the wire's length in the magnetic field, and the field strength, calculated by F = BIl sin(θ). The strength of a magnetic field created by a wire depends on the current and distance from the wire, as B = μ₀I/2πr.

Step-by-step explanation:

The force needed to pull a wire along conducting rails in a magnetic field is proportional to several factors. It involves the current flowing through the wire, the length of the wire in the magnetic field, and the strength of the magnetic field itself. According to the formula F = BIl sin(θ), where F is the magnetic force, B is the magnetic field strength, I is the current, l is the length of the wire in the field, and θ is the angle between the field and the direction of the current, we can see that this force is directly proportional to the product of B, I, and l. Specifically in regards to the magnetic field produced by a long straight current-carrying wire, it is determined experimentally and given by B = μ₀I/2πr, where I is the current, r is the distance from the wire, and μ₀ is the permeability of free space (4 x 10-7 T·m/A).

Answer 2

The force needed to pull a wire along conducting rails in a magnetic field is proportional to the product of the current flowing through the wire (I), the length of the wire segment within the magnetic field (L), and the strength of the magnetic field (B).

Step-by-step explanation:

When a current-carrying wire is placed in a magnetic field, it experiences a force known as the Lorentz force, given by the equation F = BIL, where:

- F is the force experienced by the wire,

- B is the magnetic field strength,

- I is the current flowing through the wire,

- L is the length of the wire within the magnetic field.

This equation shows that the force is directly proportional to the product of the current, length, and magnetic field strength. The direction of the force is determined by the right-hand rule, where the thumb represents the direction of the force, the forefinger represents the direction of the magnetic field, and the middle finger represents the direction of the current.

The proportional relationship indicates that if any of these factors increases, the force on the wire will also increase. For instance, increasing the current, the length of the wire in the magnetic field, or the strength of the magnetic field will result in a greater force. Understanding this relationship is fundamental in applications such as electric motors and generators, where the interaction between magnetic fields and current-carrying conductors plays a crucial role in their operation.