-Magnetic Force on a Charged Particle -Magnetic Force on a Current-Carrying Wire -Torque on a Current-Carrying Loop Fermi Lab, Chicago Illinois Circumference 6.3km Mass Spectrometer DC Motor AP Physics C Mrs. Coyle

A magnetic field can exert a force on a charged particle that moves in it.

Three ways we talk about “magnetic field”. Magnetic Field: Regions surrounding a magnet where another magnet or a moving electric charge will feel a force of attraction or repulsion. Magnetic Field Lines: exit the north pole and enter the south. Magnetic Field Strength, B Vector, Unit: Tesla, T Named after Nikola Tesla

Poles Law of Poles: Like poles repel, unlike poles attract. The force between two poles varies as the inverse square of the distance between them. A single pole (monopole) has not been isolated.

Force on a Charged Particle Moving in a Magnetic Field -Magnetic fields only exert forces on moving charged particles or other magnets.  F = |q|(v x B) = |q|vB sin q vector cross-product q is the angle between v and B F=0 for q =0 or 1800

Remember: Cross Product Using Determinants or

Remember: Properties of Cross Products of Unit Vectors ixi=0 jxj=0 kxk=0 ixj=k jxk=i kxi=j

To find the direction of the force use the Right Hand Rule For a positive test charge: Thumb v Fingers B Out of palm F The force is always perpendicular to the vB plane

For a negative particle the F is opposite to what it would be for a positive particle (use left hand)

Alternate Rule: Right Hand Curl Rule Curl fingers from v to B F = q(v x B) F is in the direction of the thumb Similarly used for the direction of torque (t=r x F)

Graphical Representation of the Magnetic Field Vector (Strength), B x field lines pointing into the page ● field lines pointing out of the page

Question Find the direction of the magnetic force acting on the +charged particle entering the magnetic field with a velocity v perpendicular to B. x x x x x V x x x x x Answer: Upwards

What motion will the particle in the previous example undergo (particle entered the B-field in a direction perpendicular to B? Circular Motion Magnetic force will represent the centripetal force http://online.cctt.org/physicslab/content/applets/JavaPhysMath/java/partmagn/index.html

Examples: http://physicslearning.colorado.edu/PiraHome/PhysicsDrawings.htm

Does the magnetic force do work? F is always perpendicular to the displacement F can change the direction of v not the magnitude F cannot do work, cannot change KE

Mass Spectrometer U.S. Department of Energy http://doegenomestolife.org

Motion of Alpha- Beta-Gamma Particles in a Magnetic Field 1) Alpha particles, positive helium nuclei, charge +2e 2) Gamma rays, (no charge) electromagnetic radiation 3) Beta particles, electrons charge -1e

Problem 1 A proton is accelerated through a constant electric field (parallel plates) and acquires kinetic energy of 4eV. It enters perpendicularly to the 2T field of a detector as shown. Charge of a proton=1.6x10-19 C, mass of proton=1.67x10-27 kg, ignore gravity. a) Draw the path of the positive charge as it enters the magnetic field.

Problem 1 cont’d b) Calculate the force acting on the charge due to the magnetic field. Charge of a proton=1.6x10-19 C , mass of proton=1.67x10-27 kg KE= 4eV B= 2T Ans: v= 2.77x104 m/s, F= 8.86x10-15 N

Problem 1 cont’d c) Calculate the distance on the detector where the particle will land (radius of the circular path). Ignore gravity. Charge of a proton=1.6x10-19 C, mass of proton=1.67x10-27 kg KE= 4eV B= 2T Ans: 1.45x10-4 m

Large Hadron Collider CERN (Conseil Européen pour la Recherche Nucléaire) Switzerland- France 2008 Circumference: 27km

Particle Accelerators use electric and magnetic fields to accelerate charged particles. Cyclotron Applet

Magnetic Force on a Current Carrying Wire F = I (L x B) = I L B sinq I is the current L is a vector of magnitude of the length of the wire and direction that of the current q is the angle formed between I and B What is the direction of the magnetic force acting on this wire? F

The force acting on a wire of arbitrary shape is the same as if it were a straight wire with the same ends The total force is:

What is the net force acting on this current-carrying loop?

Which way will a loop turn?

Forces on a Current-Carrying Loop For B as shown: F 1 = F3 = 0 F 2 = F4 = IaB Electric DC Motor (Fendt Applet)

F 2 = F4 = IaB Top View Torque Acting on the Current-Carrying Loop Torque acting on the loop:

Torque Acting on the Current-Carrying Loop

Magnetic Force on a Current Carrying Wire Lorentz Force- Magnetic Force on a Current Carrying Wire (Fendt Applet)

DC Motor

DC Motor

Problem #9 A proton moves with a velocity of v=(2i-4j+k)m/s in a region in which the magnetic field is B=(i+2j-3k)T. What is the magnitude of the magnetic force this charge experiences? Ans: 2.34x10-18 N

Problem #13 A wire 2.80 m in length carries a current of 5.00 A in a region where a uniform magnetic field has a magnitude of 0.390 T. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is (a) 60.0°, (b) 90.0°, (c) 120°. Ans: a)4.73N, b)5.46N, c)4.73N

Problem # 21 A small bar magnet is suspended in a uniform 0.250-T magnetic field. The maximum torque experienced by the bar magnet is 4.60 × 10–3 N · m. Calculate the magnetic moment of the bar magnet. Ans: 18.4mA m2

Problem #54 A 0.200-kg metal rod carrying a current of 10.0 A glides on two horizontal rails 0.500 m apart. What vertical magnetic field is required to keep the rod moving at a constant speed if the coefficient of kinetic friction between the rod and rails is 0.100? Ans: F=0.196N, B=0.039T