1. Physics for Scientists and Engineers, 3rd edition
Lecture PowerPoint
Physics for Scientists and Engineers, 3rd edition
Fishbane Gasiorowicz Thornton
© 2005 Pearson Prentice Hall
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2. The Effects of Magnetic Fields
Chapter 28
The Effects of Magnetic Fields

3. Main Points of Chapter 28 Magnets and magnetic fields; magnetic poles
Magnetic force on a point charge
Circular motion in a constant magnetic field
Lorentz force and velocity selectors
Magnetic forces on currents and current loops
Hall effect

4. 28-1 Magnets and Magnetic Fields
Forces between bar magnets:
Opposite poles attract
Like poles repel

5. 28-1 Magnets and Magnetic Fields
Magnetic field lines point from N poles to S poles
Magnetic fields can be mapped out using iron shavings:

6. 28-2 Magnetic Force on an Electric Charge
Moving electric charges are deflected by magnetic fields
By studying form and dependence of force, we find:
(28-1)

7. 28-2 Magnetic Force on an Electric Charge
The force is proportional to the charge, the velocity, the field, and the angle between the velocity and the field
The force is perpendicular to both the velocity and the field

8. 28-2 Magnetic Force on an Electric Charge
Units of magnetic field: teslas
(28-3)
The Lorentz force is the sum of the electric and magnetic forces acting on the same object:
(28-4)

9. 28-3 Consequences of the Magnetic Force on a Charge
Circular Motion in a Constant Magnetic Field
The centripetal force is provided by the magnetic field
We can solve for the radius of the circle, knowing the charge’s speed:
(28-5)

10. 28-3 Consequences of the Magnetic Force on a Charge
Interestingly, the frequency of the circular motion does not depend on the speed:
(28-7)
This is called the cyclotron frequency.

11. 28-3 Consequences of the Magnetic Force on a Charge
Velocity Selectors
A particle moving in a region where there are both electric and magnetic fields can experience no net force if:
The electric and magnetic fields are perpendicular to each other and to the particle’s velocity
The particle moves at a particular speed:
(28-9)

12. 28-3 Consequences of the Magnetic Force on a Charge
Charge-to-mass ratio of the electron
This can be measured by accelerating electrons through a known potential difference V, and then adjusting electric and magnetic fields so they are not deflected.
(28-11)

13. 28-4 Magnetic Forces on Currents
Currents consist of moving charges, so will experience force in magnetic field
Force on infinitely long wire is infinite; will look at force on wire segment instead
(28-14)
To find force on finite wire, must integrate

14. 28-4 Magnetic Forces on Currents
For a straight wire of length L making an angle θ with the magnetic field:
(28-18)
Or, defining the vector L as having the length of the wire and the direction of the current:
(28-19)

15. 28-5 Magnetic Force on Current Loops
Consider a rectangular loop in a constant magnetic field
Can easily find the force on each side of the loop
Forces cancel but, depending on orientation, there may be a torque

16. 28-5 Magnetic Force on Current Loops
We define the magnetic moment of the loop:
(28-23)
which allows us to write the torque in a simple form:
(28-22)

17. 28-5 Magnetic Force on Current Loops
The galvanometer uses this effect to measure currents:
A larger current means a larger torque.
Galvanometers are at the heart of many ammeters and voltmeters.

18. 28-5 Magnetic Force on Current Loops
A current loop in a magnetic field also has potential energy, depending on the angle it makes with the field:
(28-26)
Here, ψ is the angle between µ and B.

19. 28-6 The Hall Effect
Place a conducting strip in a magnetic field, as shown
Force on charge carriers will move them to the left, regardless of their sign
Sign of the potential difference across the strip gives the sign of the charge carriers

20. Magnetic force on a moving charge:
Summary of Chapter 28
Magnetic force on a moving charge:
(28-1)
Lorentz force:
(28-4)
A particle in a uniform magnetic field travels in a circle; its radius and frequency are:
(28-5)
(28-7)

21. Summary of Chapter 28, cont.
A particle in crossed electric and magnetic fields can experience no force if:
(28-9)
Force on an infinitesimal piece of wire:
(28-14)
And on a straight wire of length L:
(28-19)

22. Summary of Chapter 28, cont.
Torque on a current loop:
(28-22)
where
(28-24)
Potential energy of a current loop:
(28-26)