22.7 Magnetic Force on a Current-Carrying Conductor
3 min read•june 18, 2024
When a is placed in a magnetic field, it experiences a force. This force is perpendicular to both the current direction and the magnetic field. The magnitude depends on factors like current strength, conductor length, and magnetic field strength.
Understanding this interaction is crucial for many applications. Electric motors use this principle to generate rotational motion, while studies how magnetic fields interact with conducting fluids. These concepts have wide-ranging implications in technology and engineering.
Magnetic Force on Current-Carrying Conductors
Magnetic force on conductors
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- Current-carrying conductors experience a force when placed in an external magnetic field
- Force is perpendicular to both current direction and magnetic field direction
- Force is caused by interaction between magnetic field of current and external magnetic field
- Direction of force is determined by (or )
- Point thumb in direction of current
- Point fingers in direction of magnetic field
- Force will be in direction of palm
- Magnitude of force depends on several factors
- Strength of current () in amperes (A)
- Length of conductor () in magnetic field in meters (m)
- Strength of magnetic field () in teslas (T)
- Angle between current direction and magnetic field direction () in degrees
Calculation of magnetic force
- Equation for on current-carrying conductor is
- is force in newtons (N)
- is current in amperes (A)
- is length of conductor in magnetic field in meters (m)
- is magnetic field strength in teslas (T)
- is angle between current direction and magnetic field direction in degrees
- To calculate force, substitute given values into equation and solve for
- If current and magnetic field are perpendicular (), then , and equation simplifies to
- If current and magnetic field are parallel ( or ), then , and there is no force on conductor
- Example: A 2 m long wire carries a current of 5 A perpendicular to a magnetic field of 0.5 T. The force on the wire is
- The equation for can also be expressed as a
Applications of conductor-magnetic interactions
- Electric motors use magnetic force on current-carrying conductors to generate rotational motion
- Coil of wire () is placed in magnetic field
- When current is passed through coil, it experiences a torque due to magnetic force
- Torque causes coil to rotate, which can be used to drive machinery (fans, power tools)
- Magnetohydrodynamics (MHD) is study of interaction between magnetic fields and electrically conducting fluids
- MHD generators use magnetic force on moving, electrically conducting fluids to generate electricity
- Fluid (plasma or liquid metal) is passed through magnetic field
- Motion of fluid induces electric current, which can be extracted and used
- systems use magnetic force on electrically conducting fluids to generate thrust
- Magnetic field is applied to fluid
- Electric current is passed through fluid
- Interaction between current and magnetic field accelerates fluid, producing thrust (submarines, spaceships)
- MHD generators use magnetic force on moving, electrically conducting fluids to generate electricity
Electromagnetic Induction and Magnetic Flux
- is the process of generating an electric current in a conductor by changing the magnetic field around it
- is a measure of the total magnetic field passing through a given area
- Changes in through a conductor can induce an electromotive force (EMF) and current in the conductor
Key Terms to Review (16)
Armature: The armature is a crucial component in the operation of electric motors, generators, and other electromechanical devices. It refers to the rotating part of the device that carries the current-carrying windings, which interact with the magnetic field to produce torque or voltage.
Current-Carrying Conductor: A current-carrying conductor is an object, typically a wire or a metal bar, that allows the flow of electric current through it. This term is particularly relevant in the context of understanding the magnetic forces acting on such conductors and the interactions between parallel conductors carrying electric currents.
Electromagnetic Induction: Electromagnetic induction is the process by which a changing magnetic field induces an electromotive force (EMF) in a conductor, causing an electric current to flow. This phenomenon is the fundamental principle behind the operation of many electrical devices and systems, including transformers, generators, and motors.
Fleming's Left-Hand Rule: Fleming's left-hand rule is a mnemonic device used to determine the direction of the force experienced by a current-carrying conductor in a magnetic field. It provides a simple and intuitive way to visualize the relationship between the direction of the current, the magnetic field, and the resulting force.
Lorentz force: The Lorentz force is the force experienced by a charged particle moving through an electric and magnetic field. It is given by the equation $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$, 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.
Lorentz Force: The Lorentz force is the force exerted on a moving charged particle when it is placed in 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.
Magnetic flux: Magnetic flux is the measure of the quantity of magnetism, taking into account the strength and extent of a magnetic field. It is calculated as the product of the magnetic field and the area through which it passes, perpendicular to the field.
Magnetic Flux: Magnetic flux is a measure of the total amount of magnetic field passing through a given surface or area. It represents the strength and distribution of a magnetic field and is a fundamental concept in the study of electromagnetism and its applications.
Magnetic force: Magnetic force is the force experienced by a moving charge in a magnetic field. It acts perpendicular to both the velocity of the charge and the magnetic field direction.
Magnetic Force: Magnetic force is the force exerted on a magnetic object or a current-carrying conductor when placed in a magnetic field. It is a fundamental force in nature that arises from the interaction between moving electric charges and magnetic fields, and it plays a crucial role in various physical phenomena and technological applications.
Magnetohydrodynamics: Magnetohydrodynamics (MHD) is the study of the interaction between magnetic fields and electrically conducting fluids, such as plasmas, liquid metals, and ionized gases. It describes the behavior of these fluids under the influence of electromagnetic forces, and how the motion of the fluid affects the magnetic field.
MHD Generator: An MHD (Magnetohydrodynamic) generator is a device that converts the kinetic energy of an electrically conductive fluid, such as plasma or a liquid metal, directly into electrical energy through the interaction between the fluid's motion and a magnetic field. This process allows for the direct conversion of thermal energy into electricity without the need for mechanical moving parts.
MHD Propulsion: MHD propulsion, or magnetohydrodynamic propulsion, is a method of generating thrust for vehicles or vessels by using the interaction between a magnetic field and an electrically conductive fluid, such as plasma or ionized gas. This technology has potential applications in space propulsion systems and underwater vehicles.
Right-hand rule: The right-hand rule is a mnemonic used to determine the direction of angular momentum vectors. It states that if you curl the fingers of your right hand in the direction of rotation, your thumb points in the direction of the angular momentum vector.
Right-Hand Rule: The right-hand rule is a mnemonic device used to determine the direction of various vector quantities in physics, such as magnetic fields, angular momentum, and the force on a moving charge in a magnetic field. It is a simple and intuitive way to visualize the relationship between these vectors and their associated directions.
Vector Cross Product: The vector cross product, denoted as $\vec{A} \times \vec{B}$, is a binary operation in vector algebra that produces a vector that is perpendicular to both of the input vectors. The resulting vector has a magnitude equal to the product of the magnitudes of the input vectors and the sine of the angle between them, and its direction is determined by the right-hand rule.