1. An Electric Current in a Magnetic Field
A magnet exerts a magnetic force on a current-carrying wire:
B=F/IlsinQ or F=IlBsinQ
(for moving charge F=qvBsinQ)
Direction: Right-hand rule
F=0 when Q=0o
Fmax=IlB when Q=90o I Q B

2. Magnetic field is defined in terms of the force on a moving charge
B=F/qvsinQ for a moving charge
or F=qvxB
B=F/IlsinQ for a current
or F=lIxB

3. Right Hand Rule Hold your right hand open
Place your fingers in the direction of B
Place your thumb in the direction of v
The direction of the force on a positive charge is directed out of your palm
If the charge is negative, the force is opposite that determined by the right hand rule

4. only to positive charges only to negative charges
Question: The right-hand rule for the direction of the force on a charged particle in a magnetic field applies:
only to positive charges
only to negative charges
to both positive and negative charges
only when the particle is moving parallel to field.
Answer: a

5. Question: A charge particle moves perpendicularly through a magnetic field. The effect of the field is to change the particle’s
charge
mass
velocity
energy
Answer: c

6. Two charged particles of equal mass are traveling in circular orbits in a region of uniform, constant magnetic field as shown. The particles are observed to move in circular paths of radii R1 and R2 with speeds v1 and v2, respectively.
As the figure shows, the path of particle 2 has a smaller radius than that of particle 1. Which one of the following statements about this system is false?
(a) |v1/Q1| < |v2/Q2|
(b) Particle 2 carries a positive charge.
(c) Particle 1 carries a negative charge.
(d) Neither particle gains energy from the magnetic field.
(e) The particle velocities have no components parallel to the magnetic field. X

7. Magnetic Field of A Current Force between Currents Solenoid

8. Field around long, straight current
B~I/r
B=moI/2pr (r<<length of the wire)
where mo=4px10-7 T·m/A is
magnetic permeability of free space I × r
The direction of B is determined by the right-hand rule

9. Question: The magnetic field a distance d from a long, straight wire is proportional to
Answer: d

10. Example: Find the magnetic field in air 1 cm from a wire that carries a current of 1 A.
Solution: Since r=10-2 m, we have
B=moI/2pr=(4px10-7 T m/A)(1A)/2p10-2m=2x10-5 T
This is only a little smaller than the magnitude
of the earth’s magnetic field. For this reason
great care is taken aboard ships to keep
current-carry wires from magnetic compasses. I × r B

11. Question: Charged particles shown move in the vicinity of a current carrying wire. For each charged particle, indicate the direction of magnetic force due to the magnetic field generated by the wire (Arrow indicates the direction of motion of the particle, + or – indicates the sign of the charge. F - + B F I × F B F + -

12. A long, straight wire is carrying a current of 5
A long, straight wire is carrying a current of 5.0 A in the direction shown in the figure. The point P is m from the wire.
1. What is the direction of the magnetic field at point P due to the current in the wire?
(a) to the right of page (d) into the plane of the page
(b) to the left of the page (e) out of the plane of the page
(c) toward the bottom of the page
2. What is the magnitude of the magnetic field at the point P?
(a) 1.3x10–5 T (c) 2.5x10–5 T (e) 9.4x10–5 T
(b) 1.9x 10–5 T (d) 7.9x10–5 T X X

13. +Q F r I F12 F21 I F12 F21 L L r r B1=moI1/2pr B2=moI2/2pr
The fields are perpendicular to the wire, i.e., sinQ=1, Q=90o
F12=I2LB1= moI1I2L/2pr =F21=I1LB2= moI1I2L/2pr
F/L= moI1I2/2pr

14. Definition of Ampere: Definition of Ampere:
If I1=I2=1A and r=1 m
then F/L=2× N/m
1 C=1 A·s (Q=I·t)
Andre Ampere: French scientist ( )