Download Electric Field

Electric Field
Force at a distance?
We are used to forces that push or pull.
Is it possible to act on something from a distance? Consider the effects
of gravity, electricity, and magnetism.
How do they work?
Electric Fields
Michael Faraday (1791-1867) developed the idea every
charge creates “electric field” that stretches to infinity.
Interesting history:
Newton and Coloumb: action at a
distance
Faraday, Einstein: disturbance in
medium
Representation
-
+
Representation
-
+
Representation
+
-
Representation
-
+
+
Representation
-
+
Representation
-
Electric Field – vector representation
Note:
1. As our ‘test object’ gets closer
to the charged object creating
the electric field, the pull is
stronger (represented by
longer vectors)
2. The field of a negativelycharged objects pulls
positively-charged objects in
from all directions.
Electric field – lines of force
Conventions:
1) Lines of force point TOWARDS
negative charges and AWAY from
positive charges
• We are considering the force on a
positively charged ‘test object’
2) The closer the lines are together, the
stronger the force.
3) The lines represent the path a
positively-charged object would take
if released in the field.
4) Lines of force do NOT cross
5) Lines of force are perpendicular to
surface of charged objects.
Stop and think…
If an object with a charge of +1 q is represented with 8 field lines, how
many field lines should be used to represent an object with +3 q?
Justify your reasoning.
Some common configurations
Conventions for field lines
1. Draw the location and strength of the
charges
2. Draw a circle for each charge
3. Label each circle with its charge
4. Select a number of lines per charge
a) 6-8 is typically manageable
5. Draw stubs of lines on surface of charge
a) Evenly distributed
b) Proportional to charge
+5
5 C
C
-10
C
Conventions for field lines
6. Draw long range field, aka charge at
infinity
a)
Non-zero charge distribution will have
lines leaving the area
7. Connect stubs without crossing field
lines
8. Add arrows
a) Away from positive charge
b) Towards negative charge
9. Respect symmetry
Try it
Draw the electric field of a -5 C charge
separated by a short distance from a +5 C.
-5 C and +5 C.
-5
+5
Stop and think…
The photographs at right
shows charged bits of
string suspended in oil
exposed to sources of
electric charge (black
dots).
In which picture are the
charged dots the same
sign? In which picture are
the charges different?
Rationale
Field lines do not cross.
Note: field lines point
away from positive
charges
Think: what is the electric
field precisely half-way
between the two charges?
How many field lines cross
that point?
Where to put the charge?
Two electrically-charged objects (q1=+1.0x10-9C, q2=+2.0x10-9C) are
separated by 1.0 m. Where should you place a third electrically
charged object so that the net electric force on that object is zero?
Where to put the charge?
?
Here?
1 nC
No. The force from both charges
will act on the object in similar
directions.
2 nC
Where to put the charge?
1 nC
No. The force from both charges
will act on the object in similar
directions.
2 nC
?
Here?
Where to put the charge?
?
1 nC
Here?
2 nC
Yes. The force from both charges will
act on the object in opposite directions.
Also, it should be closer to smaller
charge. Why?
Where to put the charge
Two electrically-charged objects (q1=+1.0x10-9C, q2=+2.0x10-9C) are
separated by 1.0 m. Where should you place a third electrically
charged object so that the net electric force on that object is zero?
q1 = 1.0 x 10-9 C
q2 = 2q1
k = 9.0 x 109 N m2 / C2
separation = 1.0 m
r1 to object = ?
𝐹𝑛𝑒𝑡 = 𝐹𝑓𝑟𝑜𝑚 1 + 𝐹𝑓𝑟𝑜𝑚 2 = 0
So, 𝑘 𝑟
𝑞1 𝑞
1 𝑡𝑜 𝑞
2𝑞 𝑞
1
2 = 𝑘 (1.0 𝑚−𝑟)2
So, 1/𝑟 2 = 2/(1.0 𝑚 − 𝑟) 2
So, 1/𝑟 = 2/(1.0 𝑚 − 𝑟)
So, 2𝑟 = 1.0 𝑚 − 𝑟
So, r + 2𝑟 = 1.0 𝑚
1.0 m
So, r = 1+ 2 = 0.41 𝑚
Electric Potential Energy
Electric Potential Energy
Work is done to lift the
block and is converted to
potential energy.
Work is done to separate
charges and is converted
to potential energy.
Electrical Potential Energy
Work is required to bring a
positive charge closer to a
positive charge.
~ compressing a spring
Electrical potential energy
When you push q2 towards q1, it is like compressing
a spring, storing energy in the process.
How ‘stiff’ is the spring?
Coloumb’s Law tells us:
𝑞1 𝑞2
𝐹=𝑘 2
𝑟
Electrical potential energy
If you push a little harder, charge q2 moves little
closer. The tiny bit of work we did,
𝑞1 𝑞2
𝑞1 𝑞2
𝑊𝑡𝑖𝑛𝑦 = 𝑘 2 ∆𝑟𝑡𝑖𝑛𝑦 ≈ 𝑘
𝑟𝑖
𝑟𝑖
Push a little harder, it gets closer still but requires
more work.
Push still harder, it gets even closer but require
even more work.
Etc.
Electrical potential energy
Add up those tiny changes (calculus makes it easy), we find the change in
electrical potential energy to be
𝑞1 𝑞2
𝑞1 𝑞2
∆𝑈𝑞 = 𝑘
−𝑘
𝑟𝑓
𝑟𝑖
So, the potential energy between two charged objects is
𝑞1 𝑞2
𝑈𝑞 = 𝑘
𝑟
Electric potential energy vs. distance
Energy vs. distance
graph for objects with
like charges.
What would the graph
look like for opposite
charges?
Electric potential energy vs. distance
Energy vs. distance
graph for objects with
opposite charges.
Example
An electron and proton both have a charge of 1.6x10-19 C. The
distance between them is 0.53 x 10-10 m. What is the electric
potential energy between them?
G
q1 = q2 = 1.6x10-19 C
k = 9.0 x 109 N m2 / C2
r = 0.53 x 10-10 m
U
E
S
S
Uq = ?
𝑈𝑞 = 𝑘
𝑈𝑞 =
𝑞1 𝑞2
𝑟
𝑞 𝑞
𝑘 1𝑟 2
= (9.0
𝑁𝑚
x109 𝐶 2
𝑈𝑞 = 4.3 𝑥 10−18 𝐽
2
(1.6 𝑥 10−19 𝐶)(1.6 𝑥 10−19 𝐶)
)
0.53 𝑥 10−10 𝑚