Download ELECTROMAGNETISM

Magnetic Force on Freely Moving Charges
And Third Left Hand Rule
POS Checklist
 explain, qualitatively and quantitatively, how a
uniform magnetic field affects a moving electric
charge, using the relationships among charge, motion,
field direction and strength, when motion and field
directions are mutually perpendicular.
 predict, using appropriate hand rules, the relative
directions of motion, force and field in
electromagnetic interactions
Field Theory
 Any object with mass produces a gravitational
field
 The force of gravity acts in the same direction as
the G-field
 Any object with charge produces an electric field
 The force of electricity acts in the same direction
as the E-field
 Any magnet/current carrying wire produces a
magnetic field
 What direction does the magnetic force work in?
 The FB acts perpendicularly to the current and the
B-field
 This direction can be found using the 3rd Left
Hand Rule:
rd
3
Left Hand Rule
Important Facts about Fm
 Fm acts on the e¯ in
wire, not on the wire
itself
 ∴ the wire is not
required for Fm to exist
 Fm acts on any moving
charge.
Fm can act on any moving charge,
even if it is not in a wire
Formula for Magnitude of
Deflection:
Fm  qv B
 q = magnitude of charge (C)
 v⊥ = speed of the charge, ⊥ to B field (m/s)
 B = external magnetic field (T)
C mT
Note : N 
s
Fm is perpendicular to both v and B
If B  v :
then
Fm is at a max
Fm  qv B
perpendicular
If B v :
then
Fm =0
Fm  qv B
parallel
Solution:
Solution:
Solution:
Solution:
Ex. 2 A proton is moving 8.60 × 104 m/s North through a
1.20 T perpendicular magnetic field directed vertically
upward. Find its acceleration (mag and dir).
Direction of a:
Magnitude of F:
Fm  qv B
19
Fm  (1.60 10 C )(8.60 10 m / s)(1.20T )
Fm  1.6512 10
14
4
N
Acceleration
Fnet  Fm
14
Fnet 1.6512 10 N
a

27
m
1.67 10 kg
a  9.88742.... 10 m / s  9.89 10 m / s
12
2
12
2
Diploma
Diploma
Uniform Circular Motion
 If Fm is the only force on the charge
If Fm is the only force, then, Fm is Fnet
What is the direction of the acceleration?
How do you know?
Newton's 2nd Law:
a is in the same direction as Fnet
Notice that a  v
This is called centripetal acceleration.
Centripetal acceleration
Change in direction, but no change in speed. Thus it is uniform circular motion.
 Fm is called the centripetal force since it is
responsible for moving the charge in a circle
Notice that both
Fm and ac act
toward the
center of the
circle
Equation:
mv
Fc 
r
Fm  qv B
Fm  Fc
mv
qv B 
r
mv
qB 
r
2
2
Example:
 An electron traveling at 5.00 x 106 m/s enters a
magnetic field of 2.00 x 10-4 T at 90. Determine the
radius of the path followed by the electron within the
magnetic field.