Electrical Charge There are only two types of charges: (+) and (-) same type of charges repel each other. opposite type of charges attract each other. Charge is never created nor destroyed: Charge conservation one of the fundamental laws in physics (e.g. energy conservation, momentum conservation) charge (mainly (-) charge) just redistributes!! Charge comes in a discrete quantity as a multiple of e**. e = 1.602 x 10-19 C (Coulomb) one electron carries charge, –e and one proton carries charge, +e.

proton (+e) +2/3 -1/3

Conductor Insulator - - Heavy nucleus with (+) Light electrons with (-) neural atom + Conductor Insulator + - + - - - free electrons

It is expected to become a conductor at high pressure Solid Hydrogen (insulator) + - It is expected to become a conductor at high pressure above 450 GPa (4.5 Mbar). Scientists at Lawrence Livermore National Laboratory observed metallic liquid hydrogen at around 1 Mbar of pressure and around 1000 K. Read this article for more information: http://physicsworld.com/cws/article/news/5307

In conductors, electrons are mobile in the (+) charged background.  free electrons In insulators, electrons are bound around (+) charge.  Electrons cannot move freely. Most of the electrostatic phenomena are caused by redistribution of electrons (negative charge) since (+) charge is immobile. Aluminum + + + + + + + + + + + + + + + + + + + + - - - + - - - - - - - - - - - - negatively charged plastic rod still neutral!!

(+) net charge on the sphere - - - + - - - - - - - - - - Grounded (Earthed) Connected to a infinitely large charge reservoir and source. Then, disconnect from the ground  Sphere is charged by induction.

Electrons are transferred. - - - - - - - - - - - - - Now (-) charged!! Electrons are transferred.

Ex A conducting sphere is charged to have a net charge of -4 x 10-17 C. How many excess electrons are on the surface of the sphere? 250 excess electrons on the surface of the conductor!

Charges are distributed uniformly on the surface of a conductor! Copper Sphere Charges are distributed uniformly on the surface of a conductor! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Cut-out view Neutral # of positive charge = # of negative charge Transfer excess electrons  negatively charged!

- In a conductor, charges tend to distribute themselves uniformly on the surface. - - - Higher density of charges at the sharp corners.

+ = -Q (conservation of charge) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Q - - - - - - - - - - - - - - - - - + = -Q (conservation of charge) -Q/2

Ex Two identical conducting spheres carry charges of +5 mC and -17 mC. The are brought together to touch each other and Separated again. What is the amount of charge on each sphere? Is charge conserved before and after? -6 mC on each sphere The total charge before the touch is (+5) + (-17) = -12 mC and after touch 2 x (-6) = -12 mC

Q1 A conducting sphere is charged and has 108 excess electrons Q1 A conducting sphere is charged and has 108 excess electrons. How much charge is on the conductor? (1) 1.6 x 10-19 amp (2) 1.9 x 10-8 C (3) -1.6 x 10-11 C (4) -1.9 x 10-11 amp (5) -1.6 mC

Q2 Each of three objects (A, B, and C) carries a net charge Q2 Each of three objects (A, B, and C) carries a net charge. A attracts B. Objects B and C attracts each other. Which one of the following configurations is a possible combination of charge of three objects? A B C (1) + - + (2) + - - (3) - - + (4) 0 - + (5) + 0 +

Q3 Three identical conducting spheres carry net charges of +3 mC (A), +7 mC (B), and -13 mC (C). They are brought to touch together and then separated. What is the net charge on each sphere in mC? A B C (1) +3 +7 -13 (2) +7 -13 +3 (3) 0 0 0 (4) -1 -1 -1 (5) -3 -3 -3

Coulomb’s Law k = 8.988 x 109 Nm2/C2 ≈ 9.0 x 109 Nm2/C2 Q q r If q and Q are both (+) or (-), repel each other. FE > 0  repulsive FE < 0  attractive

Ex Two small conducting spheres are 0 Ex Two small conducting spheres are 0.5 m apart each other and carry net charges of +20 mC and -30 mC. What is the force acting one sphere by the other? F = -21.6 N for both spheres The (-) sign indicates that it is attractive. It does not indicate the absolute direction of the force!! The forces acting on two spheres are in the opposite direction with the same magnitude. attractive (-) sign

Ex Two identical conducting spheres are 0 Ex Two identical conducting spheres are 0.5 m apart each other and carry net charges of +20 mC and -30 mC. They were brought together to touch each other and then separated back to their original positions. What is the Coulomb force acting on each sphere? After the contact, each sphere carries -5 mC. Same total charge before (+20 – 30 = -10 mC) and after (2 x (-5) = -10 mC): conservation of charge F = +0.9 N (+) means repulsive!!

Which angle is bigger, a or b? Identical spheres + + +3 mC +10 mC Which angle is bigger, a or b? Why?

Coulomb force Gravitational force k = 9 x 109 Nm2/C2 can be repulsive and attractive! G = 6.67 x 10-11 Nm2/kg2 can only be attractive!

Ex In the hydrogen atom, a single electron exists at a distance about 0.053 nm from a proton. Find the magnitude and direction of the Coulomb force exerted on the electron by the proton. How about the gravitational force? Particle Charge (C) Mass (kg) electron -e = -1.6 x 10-19 9.11 x 10-31 proton +e = 1.6 x 10-19 1.67 x 10-27 FE = -8.2 x 10-8 N (attractive) FG = -3.63 x 10-47 N (attractive) You can completely ignore gravitational effect in atoms!!

WRONG! What is the net force on ? More than two charges? SUPERPOSE!!! -q +q a a What is the net force on ? WRONG! F = k(+q)(-q)/a2 = -kq2/a2 F = k(-q)(+q)/a2 = -kq2/a2 Fnet = F + F = -kq2/a2 + (–kq2/a2) = -2kq2/a2

Problem-solving Strategy Coulomb’s force 1. Make a clear drawing representing the problem: position of charges, distance, amount and type of charges. 2. Identify all the pairs involving the charge of interest. 3. For a given pair, determine the type of force (attractive or repulsive) from the sign of the Coulomb’s force and draw the force vector accordingly. 4. Repeat #3 for all possible pairs. 5. Do the vector sum to get the net force on the charge of interest.

Ex Two point charges of +5. 0 mC and -7 Ex Two point charges of +5.0 mC and -7.0 mC are located on the x-axis at x = 0 and x = +50 cm as shown in the figure. A third point charge with -3.0 mC is placed at x = +20 cm. What is the magnitude and direction of the force on the third charge? 0 20 cm 50 cm 5.0 mC -3.0 mC -7.0 mC Fred = 3.4 N to the left Fblue = 2.1 N to the left Ftot = Fred + Fblue = 5.5 N to the left

Ex Three equal 4. 0 mC point charges are located at (0, 0), (1 Ex Three equal 4.0 mC point charges are located at (0, 0), (1.5, 0), and (0, 3.0) in the x-y plain. The coordinates are in meters. Find the force on the charge at the origin. 1.5 m 3.0 m 4 mC q FG = 0.064 N (repulsive) FB = 0.016 N (repulsive) Ftot = 0.066 N q = tan-1(FB/FG) = 14

Q1 Which of the following statements is wrong? (1) All the excess charge on the metal is on the surface of the metal. (2) The directions of the pair of forces due to two charges are determined by the signs of the charges. (3) Conductors have many charges that are free to move about. (4) Coulomb force between two charges is inversely proportional to the distance between the charges. (5) Coulomb force is much stronger than the gravitational force.

Q2 Two identical point charges with +2 mC are placed on x = 0 and 2 m, respectively. A third charge with -30 mC is put at x = 1 m. What is the force acting on the third charge in N? (1) 0 (2) 0.54 (3) 0.036 (4) 1.08 (5) 2.16 +2 mC -30 mC 1 m