PreAP Magnetism.pdf - SchoolNotes

Permanent Magnets• All magnets have both a north and a south pole.• It is impossible to have a magnetic monopole.• Opposite poles attract.• Similar poles repel.• The north pole of a compass points towards themagnetic south pole of a magnet.• The direction of the magnetic field is defined asthe direction in which the north pole of acompass needle points.Right-Handed Coordinate SystemsyxzOut of the plane of the page.In the plane of the page.Out of the plane of the page.Into the plane of the page.Magnetic Fields Chapter 21 1Magnetic Fields Chapter 21 2Right-Handed Coordinate SystemsyNupzxWdownE+x points to the right.+y points upward.+z points out of the plane of the page.Magnetic Fields Chapter 21 3SMagnetic Fields Chapter 21 4upMagnetismout1.) A magnetic field exerts a force on a movingcharge or an electric current.leftinright2.) A moving charge or an electric currentproduces a magnetic field.The SI unit of magnetic field is a Tesla (T).downMagnetic Fields Chapter 21 5T [ = ]N[ = ] N " sA " m C " mMagnetic Fields Chapter 21 6!!

Force on an Electric Charge moving in aMagnetic FieldForce on an Electric Charge Moving in aMagnetic FieldF = qvB "F = qvB "Magnetic Fields Chapter 21 8F – Force due to magnetic field (N)q – charge ! of particle (C)v – velocity of the charged particle (m/s)B ! – magnetic field strength perpendicular to v (T)• The magnitude of the force depends upon the orientationof the velocity with respect to the magnetic field.!F = qvBsin"" - the angle between the velocity vector of thecharge and the direction of the magnetic field.• The direction ! of the force is determined using theright-hand rule. (v is crossed into B)Magnetic Fields Chapter 21 7Right-Hand Rule #11.) Orient your right hand so that youroutstretched fingers point along thedirection of the magnetic field (B).2.) Orient the thumb of your right hand so thatit points in the direction of the motion of theparticle (v).3.) The magnetic force on a positive charge isdirected out of the palm of your hand.If the charge is negative the force is in theopposite direction (or use your left hand).Magnetic Fields Chapter 21 9Motion of Charged Particles in aMagnetic FieldThe motion of a charged particle under the action of amagnetic field alone is always motion with constantspeed.The force is always perpendicular to v, so cannotchange the magnitude of the velocity, only itsdirection.!F = qvB = ma!Magnetic Fields Chapter 21 10!= m v2RForce on an Electric Current in aMagnetic FieldForce on an Electric Current in aMagnetic FieldF = IlB "F = IlB "Magnetic Fields Chapter 21 12F – Force due to magnetic field (N)l – length of ! wire in magnetic field (m)I – electric current in wire (A)B ! – magnetic field strength perpendicular to l (T)• The magnitude of the force depends upon the orientationof the current with respect to the magnetic field.!F = IlBsin"" - the angle between direction of wire and thedirection of the magnetic field.• The direction ! of the force is determined using theright-hand rule. (l is crossed into B)Magnetic Fields Chapter 21 11

Right-Hand Rule #21.) Orient your right hand so that your thumbpoints in the direction of the current in the wire.2.) Orient the the fingers of your right hand so thatthey point in the direction of the magnetic field.3.) The magnetic force on the wire is directed out ofthe palm of your hand.Magnetic Field Due to an Electric Currentin a Straight WireB = µ o2" # I rB – magnetic field strength (T)I – electric ! current in wire (A)r – distance from the wire (m)µ o – vacuum permeability (4# x 10 -7 T·m/A)Magnetic Fields Chapter 21 13Magnetic Fields Chapter 21 14Magnetic Field Due to an Electric Currentin a Straight WireRight-Hand Rule #3B = µ o2" # I rBB• The magnetic field consists of concentric circles with thewire at their center.• The direction ! of the magnetic field is determine usingthe right-hand rule #3. When the thumb points in thedirection of the current, the fingers wrapped around thewire point in the direction of the magnetic field.BrIMagnetic Fields Chapter 21 15Magnetic Fields Chapter 21 16Right-Hand Rule #3BBr BIExample 1:A positive charge with a velocity v is moving through auniform magnetic field B as shown in the figures below. Usethe right-hand rule to determine the direction of themagnetic force on the charge.vBBvvBvBMagnetic Fields Chapter 21 17Magnetic Fields Chapter 21 18

Example 2:A negative charge with a velocity v is moving through auniform magnetic field B as shown in the figures below. Usethe right-hand rule to determine the direction of themagnetic force on the charge.Example 3:A proton is moving east with a speed of 4.0 x 10 4 m/sin a uniform magnetic field with a magnitude of 2.0 Tdirected downward. Find the magnitude anddirection of the magnetic force on the proton.vBBvvBvBMagnetic Fields Chapter 21 19Magnetic Fields Chapter 21 20Example 4:An electron is moving north with a speed of 3 x 10 5 m/sin a uniform magnetic field of with a magnitude of 4 Tdirected 30˚ north of east˚. Find the magnitude anddirection of the magnetic force on the electron.Example 5:A proton with a speed of 3 x 10 5 m/s enters a uniform magneticfield with a strength of 4 T as shown below.a.)Find the acceleration of the proton when it entersthe magnetic field.b.) Draw the path of the proton after it enters the field andfind the radius of its path.c.)Repeat (a.) and (b.) for an electron.qvBMagnetic Fields Chapter 21 21Magnetic Fields Chapter 21 22Example 6:A 2.0 m long wire carries a current of 3.0 A directed tothe south. The wire passes through a region in spacein which there is a uniform magnetic field of 0.5 Tdirected to the west. Find the magnitude and directionof the force on the wire due to the magnetic field.Example 7:A 3.0 m long wire carries a current of 0.5 A towardsthe west through a uniform magnetic field. The forceon the wire due to the magnetic field is 0.20 Ndownward. What is the magnitude and direction ofthe magnetic field?Magnetic Fields Chapter 21 23Magnetic Fields Chapter 21 24

Example 8:A long wire carries a current of 2 A as shown below.Find the magnitude and direction of the magnetic fieldat points P 1 and P 2 .Example 9:A long wire carries a current of 3 A as shown below.Find the magnitude and direction of the magnetic fieldat points P 1 , P 2 , and P 3 .0.1 mP 1II0.80 m0.60 mP 20.15 mP 1P 3P 2Magnetic Fields Chapter 21 25Magnetic Fields Chapter 21 26Example 10:Two long wires perpendicular to the x-axis carry acurrents of 0.4 A as shown below. Point P 1 is locatedat the origin which is halfway between the wires andpoint P 2 is on the y-axis 0.40 m below the origin. Findthe magnitude and direction of the magnetic field atpoints P 1 and P 2 . yI 1P 10.60 m0.40 mI 2xExample 11:Two long parallel wires are separated by a distance of0.20 m and carry currents of 2 A and 4 A. Find themagnitude and direction of the force that each wireexerts on a 0.10 m section of the other ifa.) the currents are in the same direction.b.) the currents are in the opposite directions.P 2Magnetic Fields Chapter 21 27Magnetic Fields Chapter 21 28