Coils of wire with current in a magnetic field

In summary, the problem presents a wooden cylinder with a wire coil wrapped around it, released on an inclined plane with a vertical magnetic field. The goal is to find the least current through the coil that will prevent the cylinder from rolling down the plane. After considering the forces acting on the cylinder, it is determined that the net force must be zero for the cylinder to remain in equilibrium. The forces due to the current through the wires and the magnetic field are balanced, and the torque produced by the current can cause the coil to rotate without creating a new force. The angle θ is not given and will cancel out in the final calculation.
  • #1
Oijl
113
0

Homework Statement


The figure shows a wooden cylinder with mass m = 0.100 kg and length L = 0.800 m, with N = 20.0 turns of wire wrapped around it longitudinally, so that the plane of the wire coil contains the long central axis of the cylinder. The cylinder is released on a plane inclined at an angle θ to the horizontal, with the plane of the coil parallel to the incline plane. If there is a vertical uniform magnetic field of magnitude 0.250 T, what is the least current i through the coil that keeps the cylinder from rolling down the plane?

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Homework Equations





The Attempt at a Solution



I know I want a total net force of zero acting on my cylinder. This is a list of my thoughts on the problem so far:

I believe (I know) that, ignoring the wires and looking just at the wood, there is a net force on the cylinder such that it will move down the ramp.

I believe (I am very sure) that when I sent a current i through the wires, a force is produced acting "right" on the wires with the current moving away from the viewer, and a force is produced acting "left" on the wires with the current moving towards the viewer.

I believe that sending a current i through the wires will produce a net force of zero acting on the wires.

I believe that therefore the net force on the cylinder/wire object will not change when the forces due to the magnetic field are considered.

I believe (but know is false) that therefore the cylinder will move down the ramp.

I believe (I pretty much know) that the forces due to the current through the field produce a torque on the loop of wires around the cylinder - that this torque would rotate the loop until the normal vector of the loop pointed in the same direction as the magnetic field.

Since no coefficient of friction is given in this problem, friction is not to be considered.

I believe that therefore the cylinder can rotate due to torque without producing a new force that would resist its movement down the ramp.



So how can producing a net force of zero on an object that doesn't already have a net force of zero result in a net force of zero?
 
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  • #2
whether θ is given in the problem?
 
  • #3
Theta is not given. I assume that in the correct process of finding the current required to create equilibrium, theta is related to the component forces produced by the current-carrying wires. Since theta is also related to the component forces due to gravity, I figure theta will cancel out.
 
  • #4
Nevermind, I solved it.
 

1. What is a coil of wire with current in a magnetic field?

A coil of wire with current in a magnetic field is a basic electrical component that consists of a wire wound into a series of loops, or turns. When a current flows through the wire, a magnetic field is created around the coil. This magnetic field can interact with other magnetic fields, causing movement or inducing voltage in nearby conductors.

2. How does a coil of wire with current in a magnetic field work?

When a current flows through a coil of wire, it creates a magnetic field around the coils. The strength and direction of this magnetic field depends on the direction and intensity of the current. This magnetic field can interact with other magnetic fields, causing forces to act on the coil or inducing voltage in nearby conductors.

3. What is the importance of coils of wire with current in a magnetic field?

Coils of wire with current in a magnetic field are important because they are used in a variety of electrical devices. They are used in motors, generators, transformers, and many other devices. They allow for the conversion of electrical energy to mechanical energy and vice versa, making them essential components in many modern technologies.

4. How do you calculate the strength of the magnetic field in a coil of wire?

The strength of the magnetic field in a coil of wire can be calculated using the formula B = μ₀ * n * I, where B is the magnetic field strength in Tesla, μ₀ is the permeability of free space, n is the number of turns in the coil, and I is the current flowing through the coil in amperes. This formula is known as Ampere's Law and is used to determine the strength of the magnetic field at a specific point inside or outside the coil.

5. How can coils of wire with current in a magnetic field be used to generate electricity?

Coils of wire with current in a magnetic field can be used to generate electricity through electromagnetic induction. When a magnetic field moves through a coil of wire, it induces a current in the wire. This is the basic principle behind generators, where a coil of wire is rotated inside a magnetic field to produce electricity. This process can also be reversed, where electricity is used to create a magnetic field and cause movement, as seen in electric motors.

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