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

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

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

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

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

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

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

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

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

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

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