11.4 Magnetic Force on a Current-Carrying Conductor
3 min read•june 24, 2024
Current-carrying wires create magnetic fields, forming concentric circles around the wire. The field strength depends on current magnitude and distance. relates the around a closed loop to the electric current passing through it.
Magnetic forces on current-carrying wires in uniform fields are calculated using F = ILB sin θ. The determines force direction. Magnetic flux, , and dipole moments are key concepts in understanding magnetic properties and interactions.
Magnetic Fields and Forces
Magnetic fields from current-carrying wires
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- Current flowing through a wire creates a magnetic field surrounding the wire
- Magnetic field lines form concentric circles around the current-carrying wire (, )
- determines the direction of the magnetic field
- Point thumb in the current direction and fingers will curl in the magnetic field direction (, )
- Magnetic field strength is affected by the current magnitude and distance from the wire
- Directly proportional to the current: doubling the current doubles the magnetic field strength
- Inversely proportional to the distance: magnetic field weakens as distance from the wire increases (, )
- Ampère's law relates the magnetic field around a closed loop to the electric current passing through the loop
Force calculation for wires in magnetic fields
- Magnetic force on a current-carrying wire in a uniform magnetic field is calculated using
- : magnetic force measured in newtons (N)
- : current flowing through the wire in amperes (A) (circuit, appliance)
- : length of the wire segment in meters (m)
- : magnetic field strength in teslas (T) (, )
- : angle between the current direction and the magnetic field
- Maximum force occurs when the current is perpendicular to the magnetic field ()
- , simplifying the equation to
- No force is exerted when the current is parallel to the magnetic field ( or )
- , resulting in (, )
- The describes the force experienced by a charged particle moving in a magnetic field
Right-hand rule for magnetic force direction
- Right-hand rule determines the direction of the magnetic force on a current-carrying wire
- Point fingers in the current direction
- Orient palm to face the magnetic field direction
- Thumb will point in the magnetic force direction (, )
- Magnetic force is always perpendicular to both the current and the magnetic field
- Force is a cross product of the current and magnetic field vectors (, )
- Reversing either the current or magnetic field direction will reverse the force direction
- Allows for precise control of magnetic forces in applications (, particle steering)
Magnetic Properties and Interactions
- Magnetic flux represents the amount of magnetic field passing through a given area
- Permeability is a measure of a material's ability to support the formation of a magnetic field within itself
- The magnetic dipole moment characterizes the torque experienced by a magnet in an external magnetic field
Key Terms to Review (28)
Ampère's Law: Ampère's law is a fundamental principle in electromagnetism that relates the magnetic field generated by an electric current to the magnitude and direction of that current. It is one of the four Maxwell's equations, which together describe the relationships between electric and magnetic fields and electric charges and currents.
Battery: A battery is a device that converts chemical energy into electrical energy to provide a steady flow of direct current (DC). It consists of one or more electrochemical cells with external connections for powering electrical devices.
Battery: A battery is a device that stores chemical energy and converts it into electrical energy. It is a primary source of electrical power that can be used to power various electronic devices and circuits.
Compass Needle: A compass needle is a magnetized pointer that aligns itself with the Earth's magnetic field, allowing it to indicate the cardinal directions and serve as a navigation tool. It is a key component of a compass, which is an essential instrument for determining direction and orientation.
Electric Motor: An electric motor is a device that converts electrical energy into mechanical energy, producing rotational motion that can be used to power various devices and machines. It is a fundamental component in many applications, from household appliances to industrial machinery.
Electromagnet: An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Unlike permanent magnets, the magnetic field of an electromagnet can be turned on and off, and its strength can be easily controlled by adjusting the electric current.
Electromagnetic Crane: An electromagnetic crane is a type of crane that uses powerful electromagnets to lift and move heavy metal objects. These cranes rely on the magnetic force generated by an electric current flowing through a coil to pick up and transport ferromagnetic materials, such as steel or iron.
Generator: A generator is a device that converts mechanical energy into electrical energy through the process of electromagnetic induction. It is a fundamental component in the production and distribution of electrical power, playing a crucial role in various applications across the fields of magnetism, electromagnetism, and electromagnetic induction.
Generators: A generator is a device that converts mechanical energy into electrical energy through electromagnetic induction. It typically consists of a rotating coil within a magnetic field.
Hall Effect Sensor: A Hall effect sensor is a transducer that varies its output voltage in response to a magnetic field. It is used to measure the strength of a magnetic field or to detect the presence of a magnetic field. The sensor operates on the principle of the Hall effect, which is the generation of a voltage difference across an electrical conductor when a magnetic field is applied perpendicular to the direction of the current flow.
Lorentz Force: The Lorentz force is the force exerted on a charged particle when it moves through a magnetic field. It is a fundamental concept in electromagnetism that describes the interaction between electric and magnetic fields and the motion of charged particles.
Lorentz force equation: The Lorentz force equation describes the force experienced by a charged particle moving through an electric and magnetic field. It is given by $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$, where $q$ is the charge, $\mathbf{E}$ is the electric field, $\mathbf{v}$ is the velocity of the particle, and $\mathbf{B}$ is the magnetic field.
Loudspeaker: A loudspeaker is an electroacoustic transducer that converts electrical signals into audible sound waves. It is a crucial component in various audio systems, including radios, televisions, and sound systems, responsible for converting electrical energy into mechanical vibrations that produce the desired sound output.
Magnetic Field: A magnetic field is a region of space where magnetic forces can be detected. It is a fundamental concept in electromagnetism, describing the invisible lines of force that surround and permeate magnetic materials, electric currents, and changing electric fields. The magnetic field plays a crucial role in various topics within the study of college physics.
Magnetic levitation: Magnetic levitation is a phenomenon where an object is suspended in the air without any physical support, utilizing magnetic forces to counteract gravity. This technology is primarily achieved through superconductors and magnetic fields, allowing for frictionless motion and applications in transportation, such as maglev trains.
MRI machine: An MRI machine, or Magnetic Resonance Imaging machine, is a medical imaging device that uses strong magnetic fields and radio waves to generate detailed images of the organs and tissues inside the body. This technology is particularly valuable in diagnosing various medical conditions because it provides high-resolution images without the use of ionizing radiation, connecting closely to the principles of magnetic forces acting on current-carrying conductors.
Particle Accelerator: A particle accelerator is a device that uses electric and magnetic fields to propel charged particles, such as electrons, protons, or ions, to high energies and velocities. These accelerated particles are then used for various applications, including scientific research, medical treatments, and industrial processes.
Permeability: Permeability is a measure of the ability of a material to allow the passage of a fluid, such as a magnetic field or electric current, through it. It is a fundamental property that describes how easily a material can be magnetized or how easily an electric field can be established within it.
Power Lines: Power lines are high-voltage electrical transmission lines used to carry large amounts of electricity over long distances from power generation facilities to local distribution networks. They are a critical component of the electrical grid, transporting electricity efficiently and reliably to homes, businesses, and industries.
Right-hand rule: The right-hand rule is a mnemonic used to determine the direction of the magnetic field surrounding a current-carrying conductor. Point your thumb in the direction of the current and curl your fingers; your fingers indicate the direction of the magnetic field lines.
Right-Hand Rule: The right-hand rule is a mnemonic device used to determine the direction of various quantities related to electromagnetism, such as the direction of magnetic fields, the motion of charged particles in magnetic fields, and the direction of the magnetic force on a current-carrying conductor. It provides a simple and intuitive way to visualize and remember these directional relationships.
Solenoid: A solenoid is a coil of wire designed to create a uniform magnetic field in its interior when an electric current passes through it. It is commonly used in electromagnets, inductors, and valves.
Solenoid: A solenoid is a tightly wound coil of wire, often cylindrical in shape, that produces a magnetic field when an electric current passes through it. Solenoids are fundamental components in the study of electromagnetism and have applications in various areas of physics, including magnetic fields, magnetic force, and electromagnetic induction.
Tesla: The tesla (T) is the SI unit of magnetic flux density, representing the strength of a magnetic field. One tesla is defined as one weber per square meter.
Tesla: The tesla (T) is the unit of magnetic flux density, or magnetic field strength, in the International System of Units (SI). It is named after the Serbian-American inventor Nikola Tesla, who made significant contributions to the field of electromagnetism. The tesla is a fundamental unit that is essential in understanding and describing various electromagnetic phenomena and their applications.
Transformers: A transformer is a device that transfers electrical energy from one electrical circuit to another through the process of electromagnetic induction. It is a crucial component in the transmission and distribution of electrical power, allowing for the efficient transfer of energy over long distances.
Velocity selector: A velocity selector is a device that uses perpendicular electric and magnetic fields to filter charged particles based on their velocities. It ensures that only particles with a specific velocity can pass through undeflected.
Velocity Selector: A velocity selector is a device used to select charged particles with a specific velocity from a beam of charged particles. It utilizes the combined effects of electric and magnetic fields to filter out particles with undesired velocities, allowing only those with the desired velocity to pass through.