A Kingdom for a Magnet!A Kingdom for a Magnet!Finishing the topic

Next few daysNext few daysToday

◦QUIZ◦Pulling the loose ends together.◦Working some problems.

Next week – next chapter.Don’t forget the WA that is due

Sunday night.

Exam Number 2Exam Number 2

Average=67%

Loose End – Force And Loose End – Force And WiresWires

The magnetic force on themoving charges pushes thewire to the right.

Look at the direction of the Look at the direction of the force and the velocityforce and the velocity

Magnetism 5

Magnetism 6frequencyangular

cyclotron thecalled is This

v/ror r v:Recall

r

mv qvB

qvB is force magnetic Ther

mv Force lCentripeta

r

v on Accelerati lCentripeta

RECALL

2

2

2

m

Bq

r

v

Bq

mvr

Magnetism 7

Bq

mvr

m

Bq

fperiodT

f

1

2

Off AngleOff Angle

Magnetism 8

TvP

PITCH

parallel

P

PROBLEMPROBLEM

9

An electron at point A in the figure has a speed v0 of 1.4 x 106 m/s. Find

(a)the magnitude and direction of the magnetic field that will cause the electron to follow the semicircular path from A to B and

(b) the time required for the electron to move from A to B.

(c)What magnetic field would be needed if the particle were a proton instead of an electron?

m=9.1E-31 Kge=1.6E-19 C

Magnetism

Consider a section of wire.

In time t, a charge Q

passes through the wire.

F=Bqv=B Qv

In time t, a charge I t passes

through the first surface.

I= ; So Q=I tQ

t

Force

QF B Qv B tv BIL

t

Or:F=BIL Sin(I,B)

sinqvBF

sinBtvt

qF

L

I

sinILBF

Same Thing but Same Thing but angular:angular:

1+1=2 Wires1+1=2 Wires

L

II

d

Fd

LIIF

ord

LIIL

d

IBILF

d

IB

2

22

2

210

200

0

LET’S TALK ABOUT LET’S TALK ABOUT TORQUETORQUE

Current Loops in Magnetic FieldsCurrent Loops in Magnetic Fields

Magnetism 14

Current LoopCurrent Loop

Loop will tend to rotate due to the torque the field applies to the loop.

What is forceon the ends??

Magnetism 15

The Loop (From the top)The Loop (From the top)

pivot

OBSERVATION

Force on Side 2 is outof the paper and that onthe opposite side is into the paper. No net forcetending to rotate the loopdue to either of these forces.

The net force on the loop is also zero,

Magnetism 16

The other sidesThe other sides1=F1 (b/2)Sin() =(B i a) x (b/2)Sin()

total torque on the loop is: 21

Total torque:

=(iaB) bSin() =iABSin()

(A=Area)

Application: The motorApplication: The motor If the conductor is a loop, the torque can create an electric motor.

18

A circular coil of wire 8.6 cm in diameter has 15 turns and carries a current of 2.7 A. The coil is in a region where the magnetic field is 0.56 T.

What orientation of the coil gives the maximum torque on the coil.

What is this maximum torque?

Magnetism

( )NiABSin

PROBLEM SOLVINGPROBLEM SOLVING

A charge particle enters a uniform magnetic field and follows the circular path shown in the drawing.

Is the particle positively or negatively charged?

Two isotopes of carbon, carbon-12 and carbon-13, have masses of 1.993 10-26 kg and 2.159 10-26 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 7.38 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.5100 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle. 0.03 m

When a charged particle moves at an angle of 250 with respect to a magnetic field, it experiences a magnetic force of magnitude F. At what angle (less than 900) with respect to this field will this particle, moving at the same speed, experience a magnetic force of magnitude 2F?

A horizontal wire of length 0.49 m, carrying a current of 7.0 A, is placed in a uniform external magnetic field. When the wire is horizontal, it experiences no magnetic force. When the wire is tilted upward at an angle of 19° it experiences a magnetic force of 4.60 10-

3 N. Determine the magnitude of the external magnetic field.

0.00412 T

top 10.576 N bottom 20.576 N left 30 N right 40 N

A square coil of wire containing a single turn is placed in a uniform 0.20 T magnetic field, as the drawing shows. Each side has a length of 0.24 m, and the current in the coil is 12 A. Determine the magnitude of the magnetic force on each of the four sides.      

The drawing shows a thin, uniform rod that has a length of 0.35 m and a mass of 0.080 kg. This rod lies in the plane of the screen and is attached to the floor by a hinge at point P. A uniform magnetic field of 0.27 T is directed perpendicularly into the plane of the screen. There is a current I = 3.8 A in the rod, which does not rotate clockwise or counter-clockwise. Find the angle θ. (Hint: The magnetic force may be taken to act at the center of gravity.) 62.7°

A copper rod of length 0.80 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wire by an unstretched spring that has a spring constant of k = 70 N/m. A magnetic field with a strength of 0.17 T is oriented perpendicular to the surface of the table.

(a) What must be the direction of the current in the copper rod that causes the springs to stretch? The current flows left-to-right in the copper rod.

(b) If the current is 11 A, by how much does each spring stretch? 0.0107 m

Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field as in the figure below. Coil 1 has a radius of 5.2 cm and rotates in a 0.14-T field. Coil 2 rotates in a 0.42-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2? 3 cm

A wire has a length of 7.00 10-2 m and is used to make a circular coil of one turn. There is a current of 2.50 A in the wire. In the presence of a 3.00-T magnetic field, what is the maximum torque that this coil can experience? 0.00292 N · m

The rectangular loop in the drawing consists of 80 turns and carries a current of I = 2.5 A. A 1.7-T magnetic field is directed along the +y axis. The loop is free to rotate about the z axis. (θ = 31°)

(a) Determine the magnitude of the net torque exerted on the loop. 102 N · m

(b) State whether the 31° angle will increase or decrease.

the angle increases the angle decreases    

mc