Physics 1502: Lecture 2 Today’s Agenda • Announcements: – Lectures posted on: www.phys.uconn.edu/~rcote/ – HW assignments, solutions etc. • Homework #1: Homework #1: – On Masterphysics this Friday On Masterphysics this Friday • Homeworks posted on Masteringphysics – You need to register (included in cost of book) – Go to masteringphysics.com and register – Course ID: MPCOTE33308 • Labs: Begin in two weeks
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Physics 1502: Lecture 2Today’s Agenda
• Announcements:– Lectures posted on: www.phys.uconn.edu/~rcote/– HW assignments, solutions etc.
• Homework #1:Homework #1:– On Masterphysics this FridayOn Masterphysics this Friday
• Homeworks posted on Masteringphysics – You need to register (included in cost of book)– Go to masteringphysics.com and register– Course ID: MPCOTE33308
• Labs: Begin in two weeks
Today’s Topic :
• End of Chapter 20– Define Electric Field in terms of force on "test charge"
– Electric Field Lines
– Example Calculations
– Continuous charge distributions => integrate
– Moving charges: Use Newton’s law
• Demonstration of Mastering Physics
Coulomb's Law
SI Units:
• r in meters
• q in Coulombs
• F in Newtons
F12= 1
4q1q2
r2
14
= 8.987 109 N m2/C2
r
q2
r F1
2
q1
F21
r
Charles Coulomb (1736-1806)
Electric Fields
Introducing the Electric Field:
a quantity, which is independent of that charge q, and depends only upon its position relative to the collection of charges.
The force, F, on any charge q due to some collection of charges is always proportional to q:
A FIELD is something that can be defined anywhere in space
it can be a scalar field (e.g., a Temperature Field)
it can be a vector field (as we have for the Electric Field)
Lecture 2, ACT 1
• Two charges, Q1 and Q2 , fixed along the x-axis as shown, produce an electric field E at a point (x,y) = (0,d) which is directed along the negative y-axis.
– Which of the following statements is true?
(a) Both charges Q1 and Q2 must be positive.
Q2Q1 x
y
Ed
(b) Both charges Q1 and Q2 must be negative.
(c) The charges Q1 and Q2 must have opposite signs.
How Can We Visualize the E Field?
• Vector Maps:
arrow length indicates vector magnitude
+ chg
+O
• Graphs:
Ex, Ey, Ez as a function of (x, y, z)Er, E, E as a function of (r, , )
x
Ex
Example• Consider a point charge fixed at the origin of
a co-ordinate system as shown.
– The following graphs represent the functional dependence of the Electric Field.
Q x
y
r
r0
Er
0 2
Er
• As the distance from the charge increases, the field falls off as 1/r2.• At fixed r, the radial component of the field is a constant, independent of !!
E
Lecture 2, ACT 2
x
• Consider a point charge fixed at the origin of a co-ordinate system as shown.
– Which of the following graphs best represents the functional dependence of the Electric Field at the point (r,)?
Q
y
r
Fixedr>0
0 2
Ex
0 2
Ex
0 2
Ex
Another Way to Visualize E ...• The Old Way:
Vector Maps
• Lines leave positive charges and return to negative charges
• Number of lines leaving/entering charge = amount of charge
• Tangent of line = direction of E
• Density of lines = magnitude of E
+O
• A New Way: Electric Field Lines
+ chg - chg
+O O
x
y
a
a
+Q
-Q r
Electric Dipole
EE
Symmetry
Ex = ?? Ey = ??
Calculate for a pt along x-axis: (x,0)
What is the Electric Field generated by this charge arrangement?
Electric Dipole: Field Lines• Lines leave positive charge
and return to negative charge
• Ex(x,0) = 0
What can we observe about E?
• Ex(0,y) = 0
• Field largest in space betweenthe two charges
• We derived:
... for r >> a,
Field Lines from 2 Like Charges• Note the field lines from 2
like charges are quite different from the field lines of 2 opposite charges (the electric dipole)
• There is a zero halfway between charges
• r>>a: looks like field of point charge (+2q) at origin.
Lecture 2, ACT 3
• Consider a dipole aligned with the y-axis as shown.
– Which of the following statements about Ex(2a,a) is true?