F I l B In general for all wires in magnetic fields - - PowerPoint PPT Presentation

Spring 2004 OSU Magnetism Chapter 27 1

Force on a Loop

• In a uniform magnetic field a straight wire

experiences a force.

• In general for all wires in magnetic fields
• For a uniform magnetic field only the

displacement from the starting point to the ending point affects the magnetic force.

B l I F      

dF I dl B   

Spring 2004 OSU Magnetism Chapter 32 2

Force on a Loop

Practice Problem (Similar to

New HMWK Assignment)

What is the force on a semicircle shaped loop, if the straight portion has a force of 10N on it? 1) 31.4 N 4) 15.2 N 2) 10 N 5) 5 N 3) 0

Spring 2004 OSU Magnetism Chapter 27 3

Force on a Loop

Practice Problem (Similar to

New HMWK Assignment)

What is the current in the loop if the radius of curvature is 0.50m and the magnetic field is 4 T? 1) 2.5 A 3) 8.2 A 2) 1.25 A 4) 0

Spring 2004 OSU Magnetism Chapter 27 4

Torque on a Loop

• Recall
• For a uniform field to the current
• then for a force arm

to the magnetic force

F r       B l I F   



AIB IB al aIlB    ) 2 ( 2 



B A I      

F

B

b a

F I dl B   



2a F

Spring 2004 OSU Magnetism Chapter 27 5

Torque on an Electric Dipole

• Recall
• then

F r       E r q       E q F   

2a q- q+ F F

E

Spring 2004 OSU Magnetism Chapter 27 6

Magnetic Dipole Moments

• Magnetic dipole Moment
• Electric Dipole Moment

A I      B        r aq p ˆ 2   E p      

r ˆ

is a unit vector pointing from the

negative to the positive charge

Spring 2004 OSU Magnetism Chapter 27 7

Torque on a Loop Practice Problem (From New HMWK Set)

A square loop of side 0.3 m, carries a current of 2 A. It is B placed inside a magnetic I field of 0.05T. The left side

• f the loop is fixed. If the loop

is parallel to B, what is the torque on the loop about the fixed axis? 1) 0.009 N.m 3) 0.003 N.m Fixed 2) 0.018 N.m

Spring 2004 OSU Magnetism Chapter 27 8

Charge Moving in a Magnetic Field r v

B

• component of velocity will cause circular motion.
• Magnetic Force on the Charge provides the Centripetal Force

qvB F r v m  

2

qB mv r 

Cyclotron Frequency

m qB r v   



Spring 2004 OSU Magnetism Chapter 27 9

Special Case of Lorentz Force

• Lorentz Force
• When F = 0 and

B then E

p+

B v q E q F        B E v     

B E v 

Spring 2004 OSU Magnetism Chapter 27 10

Hall Effect

The magnetic force causes charge separation which shows up as a voltage

• difference. The E-field

exerts a force on the charge that balances l Magnetic Force. And the Hall Voltage is

+ + +

• +
• eH

H H d d

E eE qv B v B   

H H d

E l v Bl   e

Spring 2004 OSU Magnetism Chapter 27 11

Hall Probe

• Hall probes are used to measure the strength
• f magnetic fields.
• They are used to measure the charge carrier

concentration (from measuring the drift velocity).

• Hall Probes are small and accurate.
• They are used to determine the sign of

charge.

Spring 2004 OSU Magnetism Chapter 27 12

Mass Spectrometer

• When the velocity is known, then the mass is known by

the charge and radius of curvature in a B field. p+

E B

2

v qvB m r 

qB mv r 

Spring 2004 OSU Magnetism Chapter 27 13

2

v qvB m r 