Magnetism: Force and Field

General Characteristics Like poles repel Unlike poles attract You can never isolate a north pole from a south pole. N S N S N S N S

Earth’s Magnetic Field North pole of compass is attracted to the north. Therefore, the north pole is a magnetic south pole. Measurements have indicated that the earth’s magnetic field is decreasing. There is evidence of pole reversal at the mid-Atlantic ridge. N S

Earth’s Magnetic Field Barnes noticed a 5% reduction in the earth’s magnetic field in 130 yrs. Reversing Magnetic Field recorded in the earth’s crust. Humphreys proposes rapid reversals due to the flood.

Unique Earth Stable sun Nearly circular orbit Water present in 3 phases Magnetic field Ozone Nitrogen atmosphere Probability –10 69 to 1

Magnetic Force Magnetic fields exert forces on moving charges. Magnitude of the force is given by Direction of the force is determined by the right-hand rule. Units - Wb/m 2 or T(1T = 10 4 G)

Force on a proton Ex. What is the force on a proton traveling 60° with respect to a uniform magnetic field of 2.5 tesla at half the speed of light? Only the perpendicular component of the velocity produces a magnetic force. Will move in a helix.

Velocity Selector Lorentz Force When F = 0 and then B E p+p+

Mass Spectrometer When the velocity is known, then the mass is known by the charge and radius of curvature in a B field. p+p+ E B

Motion in a Magnetic Field component of velocity will cause circular motion. r Cyclotron Frequency v B

Cyclotron 2 sets of D magnets are set up to bend charged particles into a circular path. An alternating electric field between the D magnets causes the particles to speed up. The particles spiral outward with increasing speed. B E p+p+

Force on a Wire In a uniform magnetic field a straight wire experiences a force. In general for all wires in magnetic fields For a uniform magnetic field only the displacement from the starting point to the ending point affects the magnetic force.

Force on a Loop Ex. What is the force on a semicircle shaped loop, if the straight portion has a force of 8 N on it? What is the current in the loop if the radius of curvature is 0.75m and the magnetic field is 2 T?

Torque on a Loop Remember For a uniform field to the current then for a force arm to the magnetic force 2a F F B

Torque on a Dipole Remember then 2a qq q+ F F E

Moments Magnetic Moment Electric Dipole Moment is a unit vector going from the negative to the positive charge

Electric Energy Ex. What is the torque on a circular loop with radius of 5 cm rotating at 0.25 Hz if it has a current of 1A and is in a uniform magnetic field of 0.2 T? NS S N N S Coil Rotates

Biot-Savart Law Magnetic fields are generated by moving charge.  0 - permeability of free space I r ^ r ds

B Field for a Wire For a thin straight conductor carrying current the magnetic field is Use the right hand rule to determine the direction. (Place thumb in direction of current and B Field is in direction of fingers grabbing the wire.) Effect of moving charges is transmitted at the speed of light. Magnetism is the result of moving charges. I a

Attraction of Wires Magnetic Force of one wire interacts with the current in the other wire. This concept is used to define the Ampere and the Coulomb. Find the attraction between two wires carrying 10 A each that are 1 mm apart?

Ampere’s Law The line integral of B·ds around any closed path equals  0 I, where I is the total steady current flowing through the surface bounded by the closed path. I a

B field for a Wire Chose a closed loop which follows the magnetic field, which is constant in value. Therefore, This matches our result from using Biot- Savart Law. I r ds

B field for a Toroid A toroid is a donut shape with a coil wrapped around it. Therefore, Get a concentrated field inside the toroid. ds r

B field in a Solenoid A long wire is wound in the form of a helix. Let a solenoid consist of N turns over a distance of l. ds l

Gauss’ Law Magnetic Flux - Amount of magnetic field leaving a surface. Since magnetic field lines form loops you can never find an isolated magnetic pole.

Magnetism Sources –Orbital magnetic moment of an electron. –Spin magnetic moment of an electron. Types of Magnetism –Ferromagnetic –Paramagnetic –Diamagnetic

Ferromagnetism Consists of small regions (called domains) where the magnetic moments are aligned. Using an external magnetic field you can align the domains.

Hysteresis A remnant magnetic field remains when an external field is removed. To remove a magnetic field a oscillating magnetic field with decreasing amplitude needs to be used. B applied B internal

Magnetic Recording Iron embedded on a surface can store direction of a magnetic field.

Paramagnetism Weak interaction between magnetic moments within the material. Magnetic moments will align in the presence of an external magnetic field. If the material is lowered below the Curie temperature, it will maintain its magnetic alignment.

Diamagnetism Has no permanent magnetic moment. The presence of an external magnetic field causes a weak opposing magnetic moment in the material.

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