Chapter 33 The Magnetic Field L.A. Bumm

Mid-Term Exam 2 Wed (30 Mar) Evening 8-10pm Please use the MT2 conflict form on D2L if you absolutely cannot be take the midterm at that time. Remember that a late start is OK and preferred—but fill out the form so we will expect you. Please get the forms to me by Friday (25 Mar).

Magnetic Force Interactions This is similar to what we observed for electric forces. Electric Force: Like charges repel opposite charges attract Magnetic Force: Like poles repel opposite poles attract

Magnetism has no equivalent of charge—always dipole Magnetic monopoles, if they existed, would be analogous to positive and negative charges. However magnetic monopoles have never been observed, although they are predicted by some theories.

Magnetic Field lines We draw lines of magnetic field. Magnetic Field lines: run from North to South Always form closed loops because there is no equivalent of charge

What we call the north pole of a magnet is better termed the north seeking pole

Magnetic Field from a Current Carrying Wire An electric current creates a magnetic field around the wire. Without current: The compass needles simply point north. With current: The compass needles are tangent to a circle around the wire. Right hand rule The magnetic field B has the properties: A magnetic field is created at all points in space around a current-carrying wire. The magnetic field at each point is a vector. It has both a magnitude (magnetic field strength, B) and direction. The magnetic field exerts forces on magnetic poles. The force on a north pole is parallel to B; the force on a south pole is opposite to B.

 Looking at Vectors Tip of the arrow Tail of the arrow vector field point out of the page vector field point into of the page

Magnetic Torque on Compass Needle It can be helpful to remember that B points from north to south. So the north end of the compass needle will want to point to the south pole of the magnet and vice versa.

Current-Carrying Wire 2D view looking along wire with current pointing into the page magnetic field lines magnetic field vectors compass alignment 3D view showing the magnetic field lines and the magnetic field vectors.

Clicker Question A magnet on a pivot is free to rotate. It is placed in a uniform magnetic field pointing to the right as shown. Which way will it turn? Which way will it point? N S

Biot-Savart Law Fundamentally currents are moving charges The Biot-Savart Law describes the magnetic field from a moving charge. This is as fundamental an equation as the electric field from a point charge. SI unit of the magnetic field is the Tesla, abbreviated T. Coulombs Law and other electric equations contain the proportionality constant ε0. Magnetic equations contain the proportionality constant μ0. magnetic: permeability of free space electric: permittivity of free space

Biot-Savart Law Fundamentally currents are moving charges The Biot-Savart Law describes the magnetic field from a moving charge. This is as fundamental an equation as the electric field from a point charge. Direction of B The cross product shows that the magnetic field is mutually perpendicular to the velocity of the charge an the line between the charge and the point in space. The sign of the charge is also important. A moving negative charge produces a B in the opposite direction to a positive charge moving in the same direction. Magnitude of B The magnitude of B is proportional to q and v and the invers square of r.

Cross Product Review The cross product of C into D. Direction of the cross product: The direction of the cross product is always mutually perpendicular to both vectors. Thus perpendicular to the plane containing both vectors. Use the right hand rule to determine the direction, up or down. Align your fingers in the direction to rotate C into D. Your thumb points in the direction of the cross product. Often we say “The cross product of C into D” to emphasize the order of the cross product because that determines the direction. The magnitude of the cross product: |C × D| is proportional to the sine of the angle between the vectors.

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