1. PHY 184 Title: The Electric Field Week1 - Spring 2007 Lecture 4
1/11/07
184 Lecture 4

2. Clicker registration in lon-capa closes on January 22.
Announcements
Clicker registration in lon-capa closes on January 22.
Helproom schedule:
see LON-CAPA
Stay after the lecture today for the Honors Option.
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184 Lecture 4

3. Review - Coulomb’s Law
The electric force F between two charges, q1 and q2, separated by a distance r is given by Coulomb’s Law:
1/r2 dependence
The constant k is called Coulomb’s constant and is given by
Opposite charges: F is attractive (-)
Like charges: F is repulsive (+)
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4. E field
— QUALITATIVE
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5. The Electric Field Field Theory
The electric force is not “action at a distance” but is the action of a field.
A field is a physical entity that extends throughout a volume of space and exerts forces.
Electric field = E(x,t)
Magnetic field = B(x,t)
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6. The Electric Field (2)
A charge creates an electric field around itself and the other charge feels that field.
Electric field at a given point in space: place a positive test charge q at the point and measure the electrostatic force that acts on the test charge; then +
Test charge q +
Test charge: point object with a very small positive charge so that it does not modify the original field
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7. The Electric Field (3)
A field is not just an abstract concept that we use to describe forces. The field is real.
The electric field extends throughout space and exerts forces on charged particles.
If we place a positive point charge in an electric field, there will be a vector force on that charge in the direction of the electric field
The magnitude of the force depends on the strength of the electric field.
Field theory versus “action at a distance.”
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8. E field
— QUANTITATIVE
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9. Precise Definition of Electric Field
We define the electric field in terms of the force it exerts on a positive point charge
Unit of the electric field: N/C (newtons per coulomb)
We can then write
Note that the electric force is parallel to the electric field and is proportional to the charge
The force on a negative charge will be in the opposite direction
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10. Example – Field of a point charge
What is the field created by a point charge q?
Consider a “test charge” q0 at point x.
Force on q0:
Electric field at x:
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11. Superposition of Electric Fields
Suppose we have many charges.
The electric field at any point in space will have contributions from all the charges.
The electric field at any point in space is the superposition of the electric field from n charges is
Note that the superposition applies to each component of the field (x, y, z).
(vectors!)
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12. Electric Field Lines
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13. Electric Field Lines Unique
We can represent the electric field graphically by electric field lines — i.e., curves that represent the vector force exerted on a positive test charge.
Electric field lines will originate on positive charges and terminate on negative charges.
Electric field lines do not cross. (Why?)
The electric force at a given point in space is tangent to the electric field line through that point.
Unique
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14. Example
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15. Properties of Field Lines
The strength of the electric field is represented by the density of electric field lines
The direction of the electric field is tangent to the electric field lines
Weak
Strong
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16. Field Lines from a Point Charge
The electric field lines from a point charge extend out radially.
For a positive point charge, the field lines point outward
Terminate at infinity
For a negative charge, the field lines point inward
Originate at infinity 3D 2D
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17. Electric Field Lines for Two Point Charges
We can use the superposition principle to calculate the electric field from two point charges.
The field lines will originate from the positive charge and terminate on the negative charge. 2d 3d
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18. Determine the direction of E(x) for points on the plane half-way between the charges.
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19. Electric Field Lines from Identical Point Charges
The electric field from two identical point charges
For two positive charges, the field lines originate on the positive charges and terminate at infinity.
For two negative charges, the field lines terminate on the negative charges and originate at infinity.
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20. Determine the direction of E(x) for points on the plane half-way between the charges.
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21. General Observations about Field Lines
If the field lines connect, we have an attractive force
Imagine the charges pulling on each other
If the field lines seem to spread out, we have a repulsive force
Imagine the charges pushing each other apart
Field lines always originate on positive charge and terminate on negative charge.
Field lines never cross.
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22. Quiz Identify the charges (positive or negative) in the configuration
Positive: A, B, C
Negative D, E, F A B C D E F
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23. Demo - Electric Field Lines
Demo - visualization of electric field lines
Coulomb force
Grass seeds - +
The charge of grass seeds is redistributed by induction.
The Coulomb force makes the seeds align along the field lines.
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24. E(x) = F/q (definition) E = sum of Ei (superposition)
Summary
E(x) = F/q (definition)
E = sum of Ei (superposition)
The electric force on a charged particle q located at position x is F = q E(x).
The electric force is a field effect — not action at a distance.
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