Magnetism Lesson 28 by Owen Borville 12.29.2025
Magnetism involves the properties of magnets, the effect of the magnetic force on moving charges and currents, and the creation of magnetic fields by currents. There are two types of magnetic poles (the north magnetic pole and the south magnetic pole). North magnetic poles are those that are attracted toward the Earth's geographic north pole. Like poles repel and unlike poles attract. Magnetic poles always occur in pairs of north and south and it is not possible to isolate north and south poles.
Hans Christian Orsted and other scientists discovered that electric currents create magnetic fields, which led to the field of electromagnetism and modern electronic devices, electric motors, and magnetic imaging technology.
All magnetism is created by electric current. Ferromagnetic materials (iron) are those that exhibit strong magnetic fields. The atoms in ferromagnetic materials act like small magnets (due to currents within the atoms) and can be aligned, usually in millimeter-sized regions called domains. Domains can grow and align on a larger scale, producing permanent magnets. Such a material is magnetized, or induced to be magnetic. Above a material's Curie temperature, thermal agitation destroys the alignment of atoms, and ferromagnetism disappears. Electromagnets employ electric currents to make magnetic fields, often aided by induced fields in ferromagnetic materials.
Magnetic fields can be represented pictorially by magnetic field lines if: (1) the field is tangent to the magnetic field line (2) field strength is proportional to the line density (3) field lines cannot cross (4) field lines are continuous loops.
Magnetic fields exert a force on a moving charge q, the force of which is F = qvB and the magnitude of which is F = qvBsin θ, where θ is the angle between the directions of v and B. The SI unit for magnetic field strength B is the tesla (T), which is related to other units by 1T = 1 N/C*m/s = 1 N/A*m
The direction of the force on a moving charge is given by right hand rule (RHR-1): Point the thumb of the right hand in the direction of v, the fingers in the direction of B and a perpendicular to the palm points in the direction of F. The force is perpendicular to the plane formed by v and B. Since the force is zero if v is parallel to B, charged particles often follow magnetic field lines rather than cross them.
Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius r = mv/qB, where v is the component of the velocity perpendicular to B (magnetic field strength) for a charged particle with mass m and charge q.
The period of circular motion for a charged particle moving in a magnetic field perpendicular to the plane of motion is T = 2πm/qB
Helical motion results if the velocity of the charged particle has a component parallel to the magnetic field as well as a component perpendicular to the magnetic field.
The Hall effect is the creation of voltage ε, known as the Hall emf, across a current-carrying conductor by a magnetic field. The Hall emf is ε = Blv (where B, v, and l are mutually perpendicular) for a conductor of width l through which charges move at a speed v. Perpendicular electric and magnetic fields exert equal and opposite forces for a specific velocity of entering particles, thereby acting as a velocity selector. The velocity that passes through undeflected is v = E/B. The Hall effect can be used to measure the sign of the majority of charge carriers for metals and it can also be used to measure a magnetic field. The Hall potential is V = IBl/neA
An electrical current produces a magnetic field around the wire. The directionality of the magnetic field produced is determined by the right hand rule-2 (RHR-2), where the thumb points in the direction of the current and the fingers wrap around the wire in the direction of the magnetic field.
The magnetic force on current-carrying conductors is: F = IlBsin θ, where I is the current, l is the length of a straight conductor in a uniform magnetic field B, and θ is the angle between I and B. The force follows RHR-1 with the thumb in the direction of I.
The torque 𝜏 on a current-carrying loop of any shape in a uniform magnetic field is 𝜏 = NIABsin θ, where N is the number of turns, I is the current, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the perpendicular to the loop and the magnetic field.
The strength of the magnetic field created by current in a long straight wire is B = µ0I/2πr where I is the current, r is the shortest distance to the wire, and the constant µ0 = 4 π x 10^-7 T*m/A is the permeability of free space.
The direction of the magnetic field created by a long straight wire is determined by the right hand rule 2 (RHR-2): Point the thumb of the right hand in the direction of the current, and the fingers curl in the direction of the magnetic field loops created by it.
The magnetic field created by current following any path is the sum (or integral) of the fields due to segments along the path (magnitude and direction as for a straight wire), resulting in a general relationship between current and field known as Ampere's law.
The net force on a current-carrying loop of any plane shape in a uniform magnetic field is zero. The net torque τ on a current-carrying loop of any shape in a uniform magnetic field is τ = µB where µ is the magnetic dipole moment and B is the magnetic field strength. The magnetic dipole moment µ is the product of the number of turns of wire N, the current in the loop l, and the area of the loop A or µ = NIAn. The energy of a magnetic dipole is U = -µB
The magnetic field strength at the center of a circular loop is B = µ0I/2R where R is the radius of the loop. For a flat coil of N loops B = µ0nI/(2R). RHR=2 gives the direction of the field about the loop. A long coil is called a solenoid. The magnetic field strength inside a solenoid is B = µ0nI (n is the number of loops per unit length of the solenoid). The field inside is very uniform in magnitude and direction.
The magnetic force between two parallel currents I1 and I2 separated by a distance r has a magnitude per unit length F/l = µ0I1I2/2πr. The force is attractive if the currents are in the same direction, and the force is repulsive if the currents are in the opposite directions.
Crossed or perpendicular electric and magnetic fields act as a velocity filter, giving equal and opposite forces on any charge with drift velocity perpendicular to the fields and of magnitude v = E/B.
Applications of magnetic forces and fields are found in mass spectrometers, devices that separate ions according to their charge-to-mass ratios by first sending them through a velocity selector, then a uniform magnetic field. The charge-to-mass ratio in a mass spectrometer is q/m = E/BB0R
Cyclotrons are used to accelerate charged particles to large kinetic energies through applied electric and magnetic fields. The maximum speed of a particle in a cyclotron is v(max) = qBR/m
Magnetism involves the properties of magnets, the effect of the magnetic force on moving charges and currents, and the creation of magnetic fields by currents. There are two types of magnetic poles (the north magnetic pole and the south magnetic pole). North magnetic poles are those that are attracted toward the Earth's geographic north pole. Like poles repel and unlike poles attract. Magnetic poles always occur in pairs of north and south and it is not possible to isolate north and south poles.
Hans Christian Orsted and other scientists discovered that electric currents create magnetic fields, which led to the field of electromagnetism and modern electronic devices, electric motors, and magnetic imaging technology.
All magnetism is created by electric current. Ferromagnetic materials (iron) are those that exhibit strong magnetic fields. The atoms in ferromagnetic materials act like small magnets (due to currents within the atoms) and can be aligned, usually in millimeter-sized regions called domains. Domains can grow and align on a larger scale, producing permanent magnets. Such a material is magnetized, or induced to be magnetic. Above a material's Curie temperature, thermal agitation destroys the alignment of atoms, and ferromagnetism disappears. Electromagnets employ electric currents to make magnetic fields, often aided by induced fields in ferromagnetic materials.
Magnetic fields can be represented pictorially by magnetic field lines if: (1) the field is tangent to the magnetic field line (2) field strength is proportional to the line density (3) field lines cannot cross (4) field lines are continuous loops.
Magnetic fields exert a force on a moving charge q, the force of which is F = qvB and the magnitude of which is F = qvBsin θ, where θ is the angle between the directions of v and B. The SI unit for magnetic field strength B is the tesla (T), which is related to other units by 1T = 1 N/C*m/s = 1 N/A*m
The direction of the force on a moving charge is given by right hand rule (RHR-1): Point the thumb of the right hand in the direction of v, the fingers in the direction of B and a perpendicular to the palm points in the direction of F. The force is perpendicular to the plane formed by v and B. Since the force is zero if v is parallel to B, charged particles often follow magnetic field lines rather than cross them.
Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius r = mv/qB, where v is the component of the velocity perpendicular to B (magnetic field strength) for a charged particle with mass m and charge q.
The period of circular motion for a charged particle moving in a magnetic field perpendicular to the plane of motion is T = 2πm/qB
Helical motion results if the velocity of the charged particle has a component parallel to the magnetic field as well as a component perpendicular to the magnetic field.
The Hall effect is the creation of voltage ε, known as the Hall emf, across a current-carrying conductor by a magnetic field. The Hall emf is ε = Blv (where B, v, and l are mutually perpendicular) for a conductor of width l through which charges move at a speed v. Perpendicular electric and magnetic fields exert equal and opposite forces for a specific velocity of entering particles, thereby acting as a velocity selector. The velocity that passes through undeflected is v = E/B. The Hall effect can be used to measure the sign of the majority of charge carriers for metals and it can also be used to measure a magnetic field. The Hall potential is V = IBl/neA
An electrical current produces a magnetic field around the wire. The directionality of the magnetic field produced is determined by the right hand rule-2 (RHR-2), where the thumb points in the direction of the current and the fingers wrap around the wire in the direction of the magnetic field.
The magnetic force on current-carrying conductors is: F = IlBsin θ, where I is the current, l is the length of a straight conductor in a uniform magnetic field B, and θ is the angle between I and B. The force follows RHR-1 with the thumb in the direction of I.
The torque 𝜏 on a current-carrying loop of any shape in a uniform magnetic field is 𝜏 = NIABsin θ, where N is the number of turns, I is the current, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the perpendicular to the loop and the magnetic field.
The strength of the magnetic field created by current in a long straight wire is B = µ0I/2πr where I is the current, r is the shortest distance to the wire, and the constant µ0 = 4 π x 10^-7 T*m/A is the permeability of free space.
The direction of the magnetic field created by a long straight wire is determined by the right hand rule 2 (RHR-2): Point the thumb of the right hand in the direction of the current, and the fingers curl in the direction of the magnetic field loops created by it.
The magnetic field created by current following any path is the sum (or integral) of the fields due to segments along the path (magnitude and direction as for a straight wire), resulting in a general relationship between current and field known as Ampere's law.
The net force on a current-carrying loop of any plane shape in a uniform magnetic field is zero. The net torque τ on a current-carrying loop of any shape in a uniform magnetic field is τ = µB where µ is the magnetic dipole moment and B is the magnetic field strength. The magnetic dipole moment µ is the product of the number of turns of wire N, the current in the loop l, and the area of the loop A or µ = NIAn. The energy of a magnetic dipole is U = -µB
The magnetic field strength at the center of a circular loop is B = µ0I/2R where R is the radius of the loop. For a flat coil of N loops B = µ0nI/(2R). RHR=2 gives the direction of the field about the loop. A long coil is called a solenoid. The magnetic field strength inside a solenoid is B = µ0nI (n is the number of loops per unit length of the solenoid). The field inside is very uniform in magnitude and direction.
The magnetic force between two parallel currents I1 and I2 separated by a distance r has a magnitude per unit length F/l = µ0I1I2/2πr. The force is attractive if the currents are in the same direction, and the force is repulsive if the currents are in the opposite directions.
Crossed or perpendicular electric and magnetic fields act as a velocity filter, giving equal and opposite forces on any charge with drift velocity perpendicular to the fields and of magnitude v = E/B.
Applications of magnetic forces and fields are found in mass spectrometers, devices that separate ions according to their charge-to-mass ratios by first sending them through a velocity selector, then a uniform magnetic field. The charge-to-mass ratio in a mass spectrometer is q/m = E/BB0R
Cyclotrons are used to accelerate charged particles to large kinetic energies through applied electric and magnetic fields. The maximum speed of a particle in a cyclotron is v(max) = qBR/m