PHYS 115Exam # 3 Study Guide- A magnet that is free to rotate will rotate when another magnet is brought near.- We say there is a magnetic force between the two magnets.- A magnet experiences a magnetic force whenever it is in the magnetic field of another magnet.- Earth has a magnetic field. We call the end of a magnet that points north the north pole of the magnet, and the end that points south the south pole of the magnet.- All magnets are dipoles: They have a north and a south pole.- Like poles repel and opposite poles attract.- Magnetic field lines point from the magnet’s north pole to its south pole.- Magnetic field lines exist inside the magnet; they do NOT stop at the poles.- The magnetic dipole moment is a vector that points from the south pole of a magnet toward its north pole.- When a magnet is placed in an external magnetic field of magnitude B, the field exerts a torque on the magnet of magnitude- The torque causes the magnet to rotate.- What direction will the magnet rotate?o Point your fingers in the direction of and curl them toward the direction points.o The direction your fingers curl determines the direction the magnet rotates.- Only certain types of materials (called ferromagnetic materials) can become permanent magnets or are attracted to magnets.- A ferromagnetic object will become a permanent magnet if the magnetic dipole moments of its atoms are aligned.- A charged particle moving at a speed v in a magnetic field of magnitude B experiences a magnetic force.- Acceleration is the rate of change of velocity with time.- Velocity is a vector, so it has a magnitude (called “speed”) and a direction.- An object experiences an acceleration (i.e., a change in velocity) if its speed changes AND/OR its direction changes.- When an object is moving in a circle, the direction it is moving is constantly changing.- The acceleration that causes this change in direction is called “centripetal acceleration.”- If the object has a speed v and is moving on a circular path, then centripetal accelerationhas a magnitude v2/r.- Centripetal acceleration always points toward the center of the circle.- A wire of length L carrying a current I that is immersed in an external magnetic field B will experience a force whose magnitude is given by- Direction of this force determined by a right hand rule:o Point your fingers in the direction of the current (i.e., the direction positive charges flow).o Curl your fingers toward the direction the magnetic field points.o Your thumb points in the direction of the force of the magnetic field on the current-carrying wire.- Currents (aka, moving electric charges) create magnetic fields.- A long, straight wire carrying a current I produces a magnetic field of magnitude - The direction of the magnetic field of a long-current carrying wire is given by a right hand rule.- Solenoid: long coil of wire with the same current I passing through each loop (turn) of wire- Inside a solenoid that is very long compared to its diameter, the magnetic field has a magnitude - Direction of magnetic field inside solenoid given by a right hand rule:o Curl your fingers in the direction of the currento Your thumb points in the direction of the magnetic field.- A wire of length L carrying a current I that is immersed in an external magnetic field B will experience a force whose magnitude is given by- Direction of this force determined by a right hand rule:o Point your fingers in the direction of the current (i.e., the direction positive charges flow).o Curl your fingers toward the direction the magnetic field points.o Your thumb points in the direction of the force of the magnetic field on the current-carrying wire.- Currents (aka, moving electric charges) create magnetic fields.- A long, straight wire carrying a current I produces a magnetic field of magnitude - The direction of the magnetic field of a long-current carrying wire is given by a right hand rule.- Solenoid: long coil of wire with the same current I passing through each loop (turn) of wire- Inside a solenoid that is very long compared to its diameter, the magnetic field has a magnitude - Direction of magnetic field inside solenoid given by a right hand rule:o Curl your fingers in the direction of the currento Your thumb points in the direction of the magnetic field.- Ray model of lighto Light rays travel in a straight line until they encounter a change in mattero When they encounter a change in matter, they can be reflected or refractedo The speed of light depends on the index of refraction of the matter in which it travels v = c/n c = 3 x 108 m/s n = 1 for vacuum, n > 1 for mattero Light rays emanate from every part of an object and travel in all directions- Reflectiono Angle of incidence = angle incident ray makes with normal to the surfaceo Similarly for angle of reflection = angle of incidenceo True for curved as well as flat surfaces- Refractiono Occurs where N changeso True for curved as well as flat surfaceso Angles of incidence and refraction related by Snel’s law- Reflection at Flat Surfaceso A swim mask traps air between the glass and your eyes, so that light from outside the mask passes first through a flat layer of glass and then into air.o If surfaces are parallel, angle of incidence on second surface = angle of refraction on first surface.- Thin Lenseso Two refracting surfaces form a lens.o The optic axis of the lens is perpendicular to the lens surface and passes through its center.o A converging lens bends rays toward the optic axis; f > 0.o A diverging lens bends rays away from the optic axis; f < 0.o A lens has a focal point on each side.o Focal length depends on curvature and n- Ray tracing: converging lens, f > 0o Image location can be found by tracing at least two rays from the object.o Three rays are easy to trace:o Rays parallel to the optic axis are refracted through the far focal point.o Rays through the near focal point are refracted parallel to the optic axis.o Rays passing through the center of the lens do not bend.- Thin lens equationo 1/f = 1/s + 1/s’o Object distance s, image distance s’ and focal length f are relatedo f, s, or s’ can be positive or negativeo Magnification: s’ / s- An object placed closer to a converging lens than the lens’ focal distance (i.e. s < f ) creates a virtual image. - The rays leaving the lens appear to diverge from the image.- Converging and Diverging Lenseso A converging lens bends rays toward