1. Which of the following statements about an electric field is false?
A. It is a description of a certain property of a point in
space.
B. It is caused by the presence of electric charge.
C. It is a vector quantity, represented by lines and
arrows, with sign conventions. The lines
originate at positive charges and terminate at
negative charges.
D. It exerts a force on any other charge in it; and the force
direction is parallel (or anti-parallel) to the field lines.
E. None of the above.
5/15/17
OSU PH 213, Before Class #19

2. Which of the following statements about an electric field is false?
A. It is a description of a certain property of a point in
space.
B. It is caused by the presence of electric charge.
C. It is a vector quantity, represented by lines and
arrows, with sign conventions. The lines
originate at positive charges and terminate at
negative charges.
D. It exerts a force on any other charge in it; and the force
direction is parallel (or anti-parallel) to the field lines.
E. None of the above.
5/15/17
OSU PH 213, Before Class #19

3. Fields: Magnetic vs. Electric
The two field types also have important differences:
･ An electric field is caused by any charge.
A magnetic field is caused only by a moving charge.
･ Electric field lines originate at one point in space
(a positive charge) and terminate at another point in space
(a negative charge). Magnetic field lines form closed loops.
･ An electric field exerts a force on any charge within that
field. A magnetic field exerts a force only on a charge that
is moving within that field—with some component of its
velocity perpendicular to the field lines.
･ An electric field exerts a force parallel to the field lines.
A magnetic field exerts a force perpendicular to both the
field lines and the charge’s velocity.
5/15/17
OSU PH 213, Before Class #19

4. Magnetic Forces on Charges
Compare:
Magnitude Direction
FE = q0E (parallel to E)
Fmag = q0(v·sin)B (perpendicular to B and v)
Why sin? What’s  in this equation?
It’s the magnitude of the angle between v and B.
5/15/17
OSU PH 213, Before Class #19

5. The SI units for a magnetic field is the tesla (T).
Since Fmag = q0(v·sin)B, which of these units are equivalent to teslas?
A. J/N
B. N/J
C. N·m/(C·s)
D. N·s/(C·m)
E. None of the above.
5/15/17
OSU PH 213, Before Class #19

6. The SI units for a magnetic field is the tesla (T).
Since Fmag = q0(v·sin)B, which of these units are equivalent to teslas?
A. J/N
B. N/J
C. N·m/(C·s)
D. N·s/(C·m)
E. None of the above.
5/15/17
OSU PH 213, Before Class #19

7. Fmag = q0(v·sin)B (perpendicular to B and v)
But which perpendicular direction does Fmag have?
Use Right-Hand Rule #1:
Thumb in direction of v.
Fingers in direction of B.
Palm faces direction of Fmag on a positive q0.
Note: Fmag is opposite on a negative q0; the back of the hand
indicates its direction.
We denote B-field lines in and out of the page as  and ().
(Notice: The conventional orientation of the positive coordinate axes use RHR #1, too: The +x-axis is your thumb; the +y-axis is your fingers; the +z-axis comes up out of the page—your palm.)
5/15/17
OSU PH 213, Before Class #19

8. Example: What is the magnetic force on a proton that is traveling due east at 900 m/s in a uniform magnetic field of 2 T that is oriented due north?
Example: What is the magnetic force on a proton that is traveling due east at 900 m/s in a uniform magnetic field of 2 T that is oriented at 11.5° west of north?
What if the charge in each of the above two examples were an electron rather than a proton?
5/15/17
OSU PH 213, Before Class #19

9. Example: What is the magnetic force on a proton that is traveling due east at 900 m/s in a uniform magnetic field of 2 T that is oriented due north?
2.88 x 10–16 N upward
Example: What is the magnetic force on a proton that is traveling due east at 900 m/s in a uniform magnetic field of 2 T that is oriented at 11.5° west of north?
2.82 x 10–16 N upward
What if the charge in each of the above two examples were an electron rather than a proton? The forces would be the same magnitude, but directed downward.
5/15/17
OSU PH 213, Before Class #19

10. The Motion and Energy of a Charge in a B-Field
The magnetic force, Fmag, is always perpendicular to the velocity of the moving charge. Therefore, Fmag can act as a radial force—causing circular motion—when v and B are also perpendicular:
Fmag = q(v·sin)B = qvB = FC = mv2/r
where m is the mass of the particle with charge q.
Conclusion: r = mv/(qB)
5/15/17
OSU PH 213, Before Class #19

11. The Source of the Magnetic Field: Moving Charges
The magnetic field of a charged particle q moving with velocity v is given by the Biot-Savart law:
where r is the distance from the charge, θ is the angle between v and r, and µ0 is a universal constant (= 4p x 10–7 T·m/A).
The Biot-Savart law can be written as cross product:
5/15/17
OSU PH 213, Before Class #19