Electricity and Magnetism
• Recap:
– Confirmation of inverse square law
– Superposition principle
– Induction demo
• Electric field
Feb 13 2002
Q: Is F21 ~
y
1/r2 ?
Angle α
F21~x2
r = x1+x2
F21
x2 ~ 1/(x1+x2 )2
Check:
ln(x2) ~ -2 ln(x1+x2 )
Feb 13 2002
x1
ln(x2)
x2
x
mg
Slope = -2!
ln(x1+x2 )
Superposition principle
• Just add the forces on Q1 (as vectors)
Q3
F13
Q1
F12
Feb 13 2002
F1,total
Q2
Superposition principle
• Just add the forces on Q1!
• Works for arbitrary number of charges:
Feb 13 2002
Superposition principle
• What to do for many, many charges?
– 109 e- on glass rod...
• Replace sum with integral!
Feb 13 2002
¾Two spheres, 1 ping-pong ball
¾All conducting, neutral
1
Feb 13 2002
2
¾Approach with charged glass rod
¾Charges are induced on spheres
+ ++
+ +
+ +
+ +
++
1
Feb 13 2002
2
¾Approach with charged glass rod
¾Charges are induced on spheres
+ ++ -- ++
+ +
-- + -- ++ + +
+ -+
+
+ +
+
++
1
Feb 13 2002
+
+
2
¾Net Force on ping-pong ball
+ ++ -- ++ +
+ +
-- + -- +
+ +
+-+
+
+ +
-+
++
1
Feb 13 2002
-
+
+
2
¾Net Force on ping-pong ball
¾Attracted to sphere 1
+ ++ -- ++ +
+ +
-- + -- +
+ +
+-+
+
+ +
-+
++
-
+
+
F
1
Feb 13 2002
2
¾Ping-pong ball touches sphere 1
¾Picks up positive charge!
+ ++ --- ++ +
+ +
-+
+ +
+
-- + ++
+ +
++
-
+
+
F
1
Feb 13 2002
2
¾Ping-pong now attracted to sphere 2
+ ++ --- ++
+ +
-+ +
+
+ +
-+
++
1
Feb 13 2002
+ +
+ -
+
+
F
2
¾Ping-pong touches sphere 2
¾Picks up negative charge
+ ++ --- ++
+ +
-+ +
+
+ +
-+
++
1
Feb 13 2002
-
+
+
+
-
F
2
¾Each time, there’s less charge to pick up
¾Eventually, process comes to a halt
+ ++ --- ++
+ +
-+ +
+
+ +
-+
++
1
Feb 13 2002
-
+
+
+
-
F
2
¾Now remove rod
¾Charge on 1 and 2 equal, opposite
¾Unstable equilibrium
Feb 13 2002
- - - --
+ +
+ ++
++
1
2
¾One side wins, attracts ball
¾Ball picks up charge -> Repulsion
- - - - --
1
Feb 13 2002
+ +
+ ++
++
F
2
¾Touches other sphere
¾Continue until both spheres neutral
- - - -
1
Feb 13 2002
+ + +
+ + ++
F
2
The Electric Field
• What’s a field?
• How’s the electric field defined?
• Is it real?
Feb 13 2002
Example of Scalar Field
• Each Location X connected to a Number: T(X)
Feb 13 2002
Example of Vector Field
• Each Location X connected to a vector: v(X)
Feb 13 2002
The Electric Field
F(Q1,q,X2)
F(Q1,q,X1)
F(Q1,q,X3)
Q1
F(Q1,q,X4)
Feb 13 2002
F(Q1,q,X0)
q
The Electric Field
• Electric field is a Vector Field:
def
E(x) = F(x)/q
• For each location x, E gives Force on a ‘test
charge’ q
• We can say: Space around charge Q is
modified, such that ‘test charge’ q feels a
force F=Eq
Feb 13 2002
The Electric Field
• Superposition principle for Forces
– also true for Electric field (from Definition)
• Field from many charges is vector sum of
individual fields
– integral in limit of continous distributions
Feb 13 2002
Visualizing Fields
• One way to do it
– Color: Speed
– Line orientation,
arrow: Direction
Feb 13 2002
Visualizing the Electric Field
• Electric field ‘lines’
– Michael Faraday, 1791-1867
• Cartoon of Strength and
Direction of Field
• Line Density: Strength
• Line Orientation: Direction
(for positive test charge q)
Feb 13 2002