Download Force On A Moving Charge

MAHATMA GANDHI INSTITUTE OF TECHNICAL
EDUCATION & RESEARCH CENTER
BY
STUDENT NAME
ENROLLMENT NO
Panchal Chirag J.
140333111007
Patel Chirag H.
140333111008
Patel Shivang G.
140333111013
Patel Yagnik M.
140333111018
MAGNETIC
FORCES
Magnetic forces
The magnetic field B is defined from the Lorentz Force Law, and specifically
from the magnetic force on a moving charge:
F = qv x B
1. The force is perpendicular to both the velocity v of the charge q and the
magnetic field B.
2. The magnitude of the force is F = qv x B sin where is the angle < 180 degrees
between the velocity and the magnetic field. This implies that the magnetic force
on a stationary charge or a charge moving parallel to the magnetic field is zero.
3. The direction of the force is given by the right hand rule. The force relationship
above is in the form of a vector product.
Force On A Moving Charge
 Lorentz Force Law
 Both the electric field and magnetic field can be defined from the
Lorentz force law:

The electric force is straightforward, being in the direction of the electric
field if the charge q is positive, but the direction of the magnetic part of the
force is given by the right hand rule.
Force On A Moving Charge
Force on a Differential Current
dF = dQv x B
J
 v v
dF
J  Bdv
dF
 v  dv  v  B
dF
J  Bdv
Jdv
KdS
dQ
F

 J  B dv
 vol
F

 K  B dS
S
 v  dv
IdL
dF
K  BdS
F



dF
IdL  B
F
IL  B
I dL  B

I 

B_x_ d L
Hall Effect
E&B
 Charged particles can be subject to both electric and magnetic fields.
FM  qvB
FE  qE
FE  FM
qE  qvB
v
E
B
Deflected Current
 A wire with current has moving
charges.
l
I
q
FM
q
t
B
 Current due to electric field
 Subject to a force from
magnetism.
 The force can be related to the
current.
 Charge times velocity
FM  qvBsin 
FM 
q
vt B sin 
t
FM  IlB sin 
 Current time length
Charge Pileup
A
l
I
FE
q
FM
q
q
 nqAv
t
q
v
I
nqA
 Moving current in the magnetic
field will move carriers.
 Only carriers of current move
 Motion same for either sign
charge.
 The charges set up an electric field.
B
 Opposes magnetic force
 This is called the Hall effect.
FE  qE
FM  qvB
E  vB 
IB
nqA
Cross Potential
A
V  Ew
l
E
I
w
q
q
q
 An electric field is created in the
conductor.
 Perpendicular
magnetic field
to
current
 The electric field creates a potential V.
 Based on width w
B
V  Ew 
IB
nqx
and
 Area is width times thickness x
Carrier Sign
A
V  Ew
l
E
I
w
q
q
q
B
V  Ew 
IB
nqx
 The Hall voltage depends on the
magnetic field, current and the
charge carrier properties.
 Number density n
 Charge q
 The sign of the potential matches
the sign of the charge carriers.
 Negative for electrons
 Some conductors have positive
carriers.
Hall Probe
 The Hall effect can be used to
measure magnetic fields.
 Apply known current to known
material
 Measure Hall voltage
nqx
B
V
I
Integrity Design, Inc.
Blood Flow
 Similar to the Hall effect, the velocity of blood can be measured by its ions.
THANK YOU