charge-pp

General Physics IIGeneral Physics II

Electric Charge, Electric Charge, Forces & Fields Forces & Fields

Electric ChargeElectric Charge

� Recall that fundamental particles carry something called electric charge

� protons have exactly one unit of positive charge

�+1.602 x 10-19 Coulombs [C]

� electrons have exactly one unit of negative charge

� -1.602 x 10-19 Coulombs [C]

� Electromagnetic force is one of the basic interactions in nature

� like charges experience repulsive force

� opposite charges attracted to each other (like gravity)

Charge BalanceCharge Balance

� Neutral atoms are made of equal quantities of positive and negative charges

� Neutral carbon has 6 protons, 6 electrons, (& neutrons)

� Electrons can be stripped off of atoms

� Electrons occupy the vulnerable outskirts of atoms

� Usually charge flows in such a way as to maintain neutrality

� Excess positive charge attracts excess negative charge

� Your body has 5×1028 positive charges and 5×1028

negative charges, balanced within millions or billions

Charge SeparationCharge Separation

� Can separate charges by rubbing (contact between dissimilar materials):

� rubber on carpet

� atmosphere across ground

� silk on glass

� balloon on hair

� Insulators keep charges where they are (no flow)

� Conductors distribute charge equally on surface

� charge is free to “move about”

� why do the charges collect on the surface?

Static ElectricityStatic Electricity

� Rubbing action redistributes charge (unbalanced)

� If enough charge builds up, we get discharge

� Air spark is actually due to “breakdown” of air

� neutral air molecules separate into ions (electrons are stripped away)

� current can then flow through the “plasma-field” air

� In essence, air becomes a “wire” for a short bit

� this happens at 3 million volts per meter

�1 cm spark then at 30,000 volts

� typical finger-spark may involve a few billion electrons

Charging by ConductionCharging by Conduction• Inside a conductor charges (electrons) are free to move

� A charged object (the insulated rod) is brought near and then placed in contact with another object (the conducting sphere)

• As the rod is brought near, but prior to contact, the charges in the sphere are redistributed. Some of the electrons in the sphere are repelled from the electrons in the rod

� Upon contact, some surface electrons on the rod can move to the sphere

� When the rod is removed, the sphere is left with a charge

� The object being charged is always left with a charge having the same sign as the object doing the charging

Charging By InductionCharging By Induction

PolarizationPolarization

� This realignment of charge on the surface of an insulator is known as polarization

� Two charges, q1 and q2, separated by distance r exert a force on each other:

� ke (Coulomb’s Constant) = 8.9875 × 109 Nm2/C2, q is in Coulombs, r in meters

� Electron and proton attract each other 1040 times stronger electrically than gravitationally!� Good thing charge is usually balanced!

“Electrostatic” “Electrostatic” Force (Coulomb’s Law)Force (Coulomb’s Law)

q2q1r

221

e r

qqkF =

Coulomb Law IllustratedCoulomb Law Illustrated

� Like charges repel� Unlike charges attract

If charges are of same magnitude (and same separation),all the forces will be the same magnitude, with differentdirections....Recall Newton’s 3rd Law!

� A charged ball Q1 is fixed to a horizontal surface as shown. When another massive charged ball Q2 is brought near, it achieves an equilibrium position at a distance d12directly above Q1.

� When Q1 is replaced by a different chargedball Q3, Q2 achieves an equilibrium position at distance d23 (< d12) directly above Q3.

1a: A) The charge of Q3 has the same sign of the charge of Q1

B) The charge of Q3 has the opposite sign as the charge of Q1

C) Cannot determine the relative signs of the charges of Q3 & Q1

1b: A) The magnitude of charge Q3 < the magnitude of charge Q1

B) The magnitude of charge Q3 > the magnitude of charge Q1

C) Cannot determine relative magnitudes of charges of Q3 & Q1

Q2

Q1

gd12 d23

Q3

Q2

Example…

Two balls of equal mass are suspended from the ceiling with nonconducting wire. One ball is given a charge +3qand the other is given a charge +q.

g+q+3q

Which of the following best represents the equilibrium positions?

(b)

+3q+q

(a)

+3q+q

(c)

+3q +q

What happens when youWhat happens when youconsider more than two charges?consider more than two charges?

� What is the force on q when both q1 and q2 are present??

� The answer (just as in mechanics):

�The total force on the object is just the vector sum of the individual forces

• If q2 were the only other charge, we would know the force on q due to q2 .

• If q1 were the only other charge, we would know the force on q due to q1 .

F→

= F1→

+ F2→

F→

F1→

F2→

-q

+q1

+q2

Vector ExampleVector ExampleWhat is the net force acting on q2?

Or…….Or…….Like the net force on qLike the net force on q 33 insteadinstead

Electric FieldElectric Field

� Can think of electric force as establishing “field” telling particles which way to move and how fast

Electric “field lines” tell a positivecharge which way to move.

+

+

Run Away!

For example, a positive charge itself has field lines pointing away from it, because this is how a positively-charged “test-particle”

would respond if placed in the vicinity (repulsive force).

Electric Field Lines for a Negative Point ChargeElectric Field Lines for a Negative Point Charge

Electric Field of a Positive Point ChargeElectric Field of a Positive Point Charge

�The picture shows the electric field vector at several points.

2r

qk

q

FE

o

==r

r

** The same formula is used for the electric field strength of a negative charge **

)(C

NUnits =

Field Lines From Two Opposite Charges= Dipole

Field Lines From Two Like Charges

• There is a zero halfway between the two charges

A negative charge is placed in a region of electric fieldas shown in the picture. Which way does it move ?

a) up c) left e) it doesn't move b) down d) right

• Electric field lines leave (+) charges and return to (-) charges

• Number of lines leaving/entering charge are proportional to the amount of charge

• Field lines never cross• Field lines are always perpendicular to the charged surface

Rules for Field Lines

+ -Graphical “trick”for visualizing

E fields

•Examine the electric field lines produced by the charges in this figure.

•Which statement is true?

(a) q1 and q2 have the same sign(b) q1 and q2 have the opposite signs and q1 > q2(c) q1 and q2 have the opposite signs and q1 < q2

Two charges, q1 and q2, fixed along the x-axis as shown produce an electric field, E, at a point which is directed along the negative y-axis.

- Which of the following is true?

(a) Both charges q1 and q2 are positive

(b) Both charges q1 and q2 are negative

(c) The charges q1 and q2 have opposite signs

q1 x

y

Ed

q2

ProblemProblem

� What is the direction of the net electric field at the center of the square?

+q -2q

+2q-q

a

a

a

a

End ofEnd of

Electric Charge, Electric Charge, Forces & FieldsForces & Fields

LectureLecture

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