Motion of a charged particle in an Electric Field

► The electric force F that acts on a positive charge is parallel to the electric field E and causes the particle’s trajectory to bend in a horizontal plane. (+q is going to be pulled toward the negative plate and move toward it as it travels through this electric field… Deflected sideways.)

Motion of a charged particle in a Magnetic Field

► The magnetic force F is perpendicular to both the magnetic field B and the velocity v and causes the particle’s trajectory to bend in a vertical plane. (+q is being deflected perpendicular to F, or upward—not sideways.)

► As the charge moves upwards, the direction of the magnetic force changes, always remaining perpendicular to the magnetic field and the velocity.

Is work done while a charge moves through a magnetic field?

►Recall, W=Fd, but F and d

have to be parallel to each other.

►The magnetic force exerted on a charged particle is alwaysgoing to be perpendicular to its displacement so work is never done by a magnetic field to change the Kinetic Energy of a charged particle.

►The magnetic force does alter the particle’s direction.

The motion of a charged particle in a constant magnetic field…

► For a special case when velocity is exactly perpendicular to the magnetic field, the magnetic force causes the particle to move in a circular path.

►Note: x denotes that B points into page, and

► denotes that B points out

of page (like an arrow).

►Recall that Centripetal Force = Fc = mac = mv2/r

►And, F =B q (vsin)

►Bq(vsin)= mv2/r

►And since v in this case is perpendicular (90o) to B, then (sin90o)= 1, so

►Bqv= mv2/r, or

► r = mv/(Bq)

►Radius is inversely proportional to B

►Stronger fields produce tighter circles!

The magnetic force is perpendicular to both the magnetic field and the velocity. The perpendicular force will bend the path of the charge remaining in the uniform magnetic field.

The magnetic force on a negative charge is in the opposite direction.

The magnetic force provides the centripetal force to bend the charge into a circle

The Mass Spectrometer

►An instrument used to identify unknown elements, molecules and relative abundance of isotopes.

►An Instrument used by physicists, chemists and anesthesiologists.

►Anesthesiologists use a Mass Spectrometer during surgery where they provide information on the gases, including the anesthetic, in the patient’s lungs.

How does a Mass Spectrometer Work?

►Sample is vaporized and then ionized by removing an electron (becoming positive).

►The positive ions are accelerated through a voltage, V.

►With speed, v, the ions pass through a hole in the metal plate and enter a region of constant magnetic field, B.

►The ions are deflected at various radii based on mass and velocity.

The basic features of a mass spectrometer. The dashed lines are the paths traveled by ions of different masses. Ions with mass mfollow the path of radius r and enter the detector. Ions w/larger

mass m1 follow the outer path and miss the detector.

►Recall, for a particle moving in a circular path through a magnetic field: r = mv /(qB)

► So, for a particle that is charged by removing one electron, q=the charge of a proton or the positive charge of an electron

► r = mv /(e B), where e = +1.6X10-19C►And, since the KE of the particle is increased as it

goes from the ion source through the metal plate where it receives a change in potential of amount V then,

►KE = EPE or KE = Vq►And, since the particle starts with no velocity and

no voltage: KE=KEf, and V=Vf, so…►½mv2 = Vq rearrange and solve for v:► v = (2qV/m) and since q = e► v = (2eV/m)

► r = mv/(e B), and v = (2eV/m)

► r = m((2eV/m) / (e B), solve for m:

► m = (e r2 B2)/(2V) or

►m= [(e r2)/(2V)] B2

► For a positively charged particle, by keeping the radius and potential V constant, the only way a mass is going to make it into the detector is by adjusting the magnetic field, B, for that particular mass, m, value.

► So, B is adjusted and then used in the calculation to determine the mass of a particle arriving at the detector.

How a speaker works:

► (a) An “exploded” view of one type of speaker design, which shows a cone that can vibrate back and forth (pushing & pulling on air in front of it, creating sound waves), a voice coil, and a permanent magnet.

► (b) Because of the current in the voice coil (shown as x and ), the magnetic field causes a force F to be exerted on the voice coil and cone; causing both to move.

Fig. 21.19

Using Electromagnetism for Propulsion

► http://northeastmaglev.com/the-train

Basic Design of

a DC motor:

(a) When a current exists in a coil, the coil experiences a torque. (b) Because of its inertia, the coil continues to rotate when there is no current.

Current carrying wires exert magnetic forces on one another.

► (a) Two long, parallel wires carrying currents I1

and I2 in opposite directions repel each other.

► (b) The wires attract each other when the currents are in the same direction.

(a) The field lines around the bar magnet resemble those around the loop in Fig 21.30a.

(b) The current loop can be imagined to be a phantom bar magnet w/a north pole and a south pole.

(a) The two current loops attract each other if the directions of the currents are the same and (b) repel each other if the

directions are opposite. The “phantom” magnets help explain the attraction and repulsion.

Which will repel, which will attract?

Which will repel, which will attract?a) Repel, b) Repel a) Attract, b) Repel

Ns

NS

S N S N

N S S N

Determine whether each particle is positive, negative or neutral.

Using RHR #1, the answer is…► Particle #1 is…

► Positively charged!

► Particle #2 is…

►Neutral (no charge)

► Particle #3 is…

►Negatively charged!

Three particles of identical charge and mass enter a constant magnetic field, B. Which

particle is moving fastest??? Slowest?

And the answer is…► Fc = mac = mv2/r

► And, F =B q (vsin) = Bqv (because sin90o= 1)

► Bqv = mv2/r

► Bqv= mv2/r, or

► r = mv/(Bq)

► And since m, B, & q are the same in all three scenarios…

► r v

► particle #1 with the largest radius is traveling fastest!

The drawing shows a top view of four interconnected chambers. A negative charge is fired into chamber 1. By turning on separate magnetic fields in each chamber, the charge can be made to exit from chamber 4. a) Describe how the magnetic field in each chamber should be directed. b) If the speed of the charge is v when it enters chamber 1, what’s the speed when it exits chamber 4? Why?

Using RHR #1 for a Negative Charge:

►Region 1: B is directed into page

►Region 2: B is directed out of page

►Region 3: B is directed out of page

►Region 4: B is directed into page

►KE is conserved & unchanged…

► v exiting equals v entering.

The drawing shows a conducting wire wound into a helical shape. The helix acts like a spring and expands back toward its original shape after its coils are squeezed together and released. The

bottom end of the wire just barely touches the mercury (a good electrical conductor) in the cup. After the switch is closed, current in the circuit causes the light bulb to glow. Does the bulb glow

continually, glow briefly and then go out, or repeatedly turn on and off like a turn signal on a car? Explain.

The bulb flashes on and off…

Torque on Dipoles

►Torque is defined as: T = F ● L force and lever arm need to be perpendicular.

►We can sub in

►F = I L B sin for force to get:

►T = IAB sin

►Torque is max when is 900

Angle and Dipole Moment