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Charge Properties • Conservation – Charge is not created or destroyed, only transferred. – The net amount of electric charge produced in any process is zero. Charge Properties • Conservation – Charge is not created or destroyed, only transferred. – The net amount of electric charge produced in any process is zero. • Quantization – The smallest unit of charge is that on an electron or proton. (e = 1.6 x 10-19 C) • It is impossible to have less charge than this • It is possible to have integer multiples of this charge Charge Properties • Conservation – Charge is not created or destroyed, only transferred. – The net amount of electric charge produced in any process is zero. • Quantization – The smallest unit of charge is that on an electron or proton. (e = 1.6 x 10-19 C) • It is impossible to have less charge than this • It is possible to have integer multiples of this charge What is meant by quantization of charge? • Discovered in 1911 by Robert A. Millikan in the oil drop experiment • The unit of charge is so tiny that we will never notice it comes in indivisible lumps. The fact that charge comes in discrete amounts, only divisible by a constant, is what is meant by quantization. • Example: Suppose in a typical experiment we charge an object up with a nanoCoulomb of charge (Q = 10-9 C). How many elementary units of charge is this? Elementary unit of charge = 1 particle (a proton or electron) 1 × 10 −9 C × 1unit, or particleof charge = 0.625 x 1010 = 6.25 x 109 particles 1.6 × 10 −19 C Six billion units of charge!! € Conductors and Insulators • Conductor • Insulator • Semiconductor transfers charge on contact does not transfer charge might transfer charge Calculating the Magnitude of Electrical Force Look familiar? Compare Similarities: Both equations show an inverse square relationship between force and separation distance. And both equations show that the force is proportional to the product of the quantity that causes the force - charge in the case of electrical force and mass in the case of gravitational force. Differences: First, a comparison of the proportionality constants - k versus G - reveals that the Coulomb's law constant (k) is significantly greater than Newton's universal gravitation constant (G). Subsequently, a unit of charge will attract a unit of charge with significantly more force than a unit of mass will attract a unit of mass. Second, gravitational forces are only attractive; electrical forces can be either attractive or repulsive. Direction Coulomb's Law • The force between two charges gets stronger as the charges move closer together. • The force also gets stronger if the amount of charge becomes larger. Coulomb's Law • The force between two charges is directed along the line connecting their centers. • Electric forces always occur in pairs according to Newton’s third law, like all forces. Coulomb's Law • The force between charges is directly proportional to the magnitude, or amount, of each charge. • Doubling one charge doubles the force. • Doubling both charges quadruples the force. Coulomb's Law • Doubling the distance reduces the force by a factor of 22 = (4), decreasing the force to one-fourth its original value (1/4). • This relationship is called an inverse square law because force and distance follow an inverse square relationship. • The force between charges is inversely proportional to the square of the distance between them. Q values are often on the order of 10-9 or possibly 10-6 Coulombs. For this reason, charge is often expressed in units of microCoulomb (µC) and nanoCoulomb (nC). If a problem states the charge in these units, it is advisable to first convert to Coulombs prior to substitution into the Coulomb's law equation. The following unit equivalencies will assist in such conversions: 1 Coulomb = 106 µC (microCoulomb) 1 Coulomb = 109 nC (nanoCoulomb) Calculating force • Two balls are each given a static electric charge of one tenthousandth (0.0001) of a coulomb. • Calculate the force between the charges when they are separated by one-tenth (0.1) of a meter. • Compare the force with the weight of an average 70 kg person. • Two balls are each given a static electric charge of one tenthousandth (0.0001) of a coulomb. • Calculate the force between the charges when they are separated by one-tenth (0.1) of a meter. • Compare the force with the weight of an average 70 kg person. F = 9000 N away from each other Fg = mg = 70 kg (9.8 m/s2) = 686 N • The weight of a 70 kg person: • F = mg = (70 kg)(9.8 N/kg) = 686 N • The force between the charges is 13.1 times the weight of an average person! (9,000 ÷ 686). Coulomb’s Law Two Positive Charges • What is the magnitude of the force between a positive & negative charge, each 1 nanoCoulomb, and 1cm apart? q2 q1 r 1 nC 1 nC 1 cm (Equivalent to the weight of a long strand of hair) • What is the direction of the force? 1 nC 1 cm 1 nC Some atoms hold on to their electrons more tightly than others do. How strongly matter holds on to its electrons determines its place in the triboelectric series. If a material is more apt to give up electrons when in contact with another material, it is more positive in the triboelectric series. If a material is more apt to "capture" electrons when in contact with another material, it is more negative in the triboelectric series. The following table shows you the triboelectric series for many materials you find around the house. Positive items in the series are at the top, and negative items are at the bottom: Human hands (usually too moist, though) Very positive Rabbit Fur Glass Human hair Nylon Wool Fur Lead Silk Aluminum Paper Cotton Steel _____________________________________________Neutral _________ Wood Amber Hard rubber Nickel, Copper Brass, Silver Gold, Platinum Polyester Styrene (Styrofoam) Saran Wrap Polyurethane Polyethylene (like Scotch Tape) Polypropylene Conductors and Insulators • Conductor • Insulator • Semiconductor transfers charge on contact does not transfer charge might transfer charge Conductors and Insulators 3 ways to charge objects 1. Charging by Friction Human hands (usually too moist, though) Very positive Rabbit Fur Glass Human hair Nylon Wool Fur Lead Silk Aluminum Paper Cotton Steel _____________________________________________Neutral _________ Wood Amber Hard rubber Nickel, Copper Brass, Silver Gold, Platinum Polyester Styrene (Styrofoam) Saran Wrap Polyurethane Polyethylene (like Scotch Tape) Polypropylene 2. Charging by Induction 3. Charging by Conduction Electroscope The electroscope typically consists of a conducting plate or knob, a conducting base and either a pair of conducting leaves or a conducting needle. Charging by Conduction (cont’d) Electroscopes Electroscope Example • Suppose that a negatively charged balloon is used to charge an electroscope. • Explain, in terms of electron movement, what is happening in each step. Coulomb’s Law Where Q1 and Q2 are the amount of charge and k is a proportionality constant Charges produced by rubbing ordinary objects (such as a comb or a plastic ruler) are typically around a microcoulomb or less: Coulomb’s Law The charges carried by the proton and electron are equal in size. However, the mass of the proton is 2000 times the mass of the electron. Example Suppose you could place a free proton on the ground, and wished to place a second one directly above the first so that the weight of the second proton would be exactly balanced by the electric repulsion between them. How far apart must the protons be? 0.12 m Defining Electric Field Strength • Electric field strength is a vector quantity • An electric charge, Q, creates an electric field. We will refer to this electric charge as the source charge. • The strength of the source charge's electric field could be measured by any other charge placed somewhere in its surroundings. The charge that is used to measure the electric field strength is referred to as a test charge, q. • A force, F, is felt by the test charge q. Electric Field Strength • The magnitude of the electric field is simply defined as the force per charge on the test charge. Units of N/C Another equation for E • The electric field strength is not dependent upon the quantity of q • In the formula for electric field strength E = F/q, substitute Coulomb’s Law in for F • • q was cancelled from both numerator and denominator of the equation. The new formula shows that the electric field strength is dependent upon – the quantity of charge on the source charge (Q) and – the distance of separation (d) from the source charge. Example 2 • Tiny droplets of oil acquire a small negative charge while dropping through a vacuum (pressure = 0) in an experiment. An electric field of magnitude 5.92 x 104 N/C is present. a) One particular droplet is observed to remain suspended against gravity. If the mass of the droplet is 2.93 x 10-15 kg, find the charge carried by the droplet. b) Another droplet of the same mass falls 10.3 cm from rest in 0.250 s, again moving through a vacuum. Find the charge carried by the droplet. First, lets draw a picture. Which way must the arrows be pointing in my electric field? Example 2 • Tiny droplets of oil acquire a small negative charge while dropping through a vacuum (pressure = 0) in an experiment. An electric field of magnitude 5.92 x 104 N/C is present. a) One particular droplet is observed to remain suspended against gravity. If the mass of the droplet is 2.93 x 10-15 kg, find the charge carried by the droplet. E mg = Fe = Eq (2.93 × 10 −15 kg)(9.8m /s2 ) q = mg / E = −5.92 × 10 4 N /C = - 4.85 x 10-19 C € Example 2 • Tiny droplets of oil acquire a small negative charge while dropping through a vacuum (pressure = 0) in an experiment. An electric field of magnitude 5.92 x 104 N/C points straight down. b) Another droplet of the same mass falls 10.3 cm from rest in 0.250 s, again moving through a vacuum. Find the charge carried by the droplet. Fe F = ma = F - F net e = Eq - mg g Now find the acceleration, a, of the droplet. Δy = vit + ½ at2 a = 2Δy/t 2= € Fg 2(−0.103m) 2 = -3.3 m/s 0.25 2 sec 2 ma + mg (2.93 × 10 −15 kg)(−3.3m /s2 + 9.8m /s2 ) -19 C = 3.22 x 10 = q= −5.92 × 10 4 N /C E € Equations - Summary • Coulomb’s Law – units: N • Electric Field Strength – units: N/C • Electric Field Strength (a second equation) There is a parallel (similarity) between g and E € A note about k It was pointed out (by a scientist long ago) that k can be written in terms of 1/4π and a new constant, ε : 1 k= 4 πε Where ε is called the permittivity. Materials with high ε are easily polarized and, therefore, good electric insulators (electric insulators cancel E fields). When the charges (q) are in air (similar enough to a vacuum), ε is written as ε0 . This has been the assumption for the cases/equations discussed so far. So, in the equations (for Coulomb’s Law and E field), k can be written as k0 : 1 k0 = 4 πε 0 where εo = 8.8541878 x 10-12 C2/Nm2 So, you may see Coulomb’s Law written as: Q1Q2 = k0 2 r And Electric Field Intensity: € 2 Q2 = k0 2 r But if the experiment is performed in a medium other than air, we use a tabulated value of ε instead of the εo in ko Where Q1 is the test charge, and Q2 is the source charge. Example 3 A point-charge of 10 µC is surrounded by water (permittivity is 7.1 x 10-10 C2/Nm2). Calculate the magnitude of the electric field 20 cm away. −6 ⎞ ⎛ 1 10 × 10 C 1 Q= Q ⎜ ⎟ −10 2 2 E =k 2 = 2 4 π (7.1 × 10 ) ⎝ 0.2 m ⎠ 4 πε r r € E = 28,020.2 N/C € € Charge cannot be transferred through air Electric Fields • All charged objects create an electric field which extends outward into the space which surrounds it. • The charge alters that space, causing any other charged object that enters the space to be affected by this field. • The strength of the electric field is dependent upon how charged the object creating the field is and upon the distance of separation from the charged object. • Electric force acts through a field. • An electric field is a region in space around a charged object that causes a stationary charged object to experience an electric force. • One way to show an electric field is by drawing electric field lines. • Electric field lines point in the direction of the electric force on a positive charge. • The electric field lines around a positive charge point outward. • The electric field lines around a negative charge point inward. Electric Field Lines Electric Field Lines • Electric field lines never cross one another. • Field lines show both the direction of an electric field and the relative strength due to a given charge. • More lines are drawn for greater charges to indicate greater force. Direction of Electric Fields • By convention, the test charge is assumed positive when assigning direction arrows to field lines. • Since like charges repel and opposites attract, electric field vectors will always point – away from positive source charges – toward negative source charges • Electric Field lines do not cross • The electric field is stronger when the lines are located closer to one another. Electric Field Lines Like charges (++) Opposite charges (+ -) This is called an electric dipole. Electric Field Lines Examples What is the direction of the electric field at point C? 1) Left 2) Right 3) Zero y C x Examples What is the direction of the electric field at point C? 1) Left Red is negative 2) Right Blue is positive 3) Zero Away from positive charge (right) Towards negative charge (right) Net E field is to right. y C x Comparison: Electric Force vs. Electric Field • Electric Force (F) - the actual force felt by a charge at some location. • Electric Field (E) - found for a location only – tells what the electric force would be if a charge were located there. • Both are vectors, with magnitude and direction. Add x & y components. Examples What is the direction of the electric field at point A? 1) Up 2) Down 3) Left 4) Right 5) Zero A y B x Examples What is the direction of the electric field at point A? 1) Up Red is negative 2) Down Blue is positive 3) Left 4) Right 5) Zero A y B x Examples What is the direction of the electric field at point A, if the two positive charges have equal magnitude? 1) Up 2) Down 3) Right 4) Left 5) Zero A y B x Examples What is the direction of the electric field at point A, if the two positive charges have equal magnitude? 1) Up Red is negative 2) Down Blue is positive 3) Right 4) Left A 5) Zero x Concept Check Example 4 A positive point charge +q is fixed in position at the center of a square, as the drawing shows. A second point charge is fixed to either corner B, corner C, or corner D. The net electric field at corner A is zero. (a) At which corner is the second charge located? (b) Is the second charge positive or negative? (c) Does the second charge have a greater, a smaller, or the same magnitude as the charge at the center? Example 5 Two point charges q1 = -6.15 nC, and q2 = -10.5 nC are separated by 25.0 cm. (a) Find the net electric field these charges produce at point A. (b) Find the net electric field these charges produce at point B. EA = 6990 N/C, to right EB = 6306.4 N/C = 6310 N/C, to right Example 6 A proton travels horizontally to the right at 4.50 x 106 m/s. a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of 3.20 cm. Note: mp= 1.67 x 10-27 kg, qp = 1.6 x 10-19 b) How much time does it take the proton to stop after entering the field? Use v 2 = v 2 + 2ax f i ma −v i 2 −(4.5 × 10 6 ) 2 F = ma = Eq → E = , where a = = q 2x 2(0.032m) v f − vi t= since v f = v i + at 2 a 0 − 4.5 × 10 6 t= −3.16 × 1014 E = 3.3 x 106 N/C, left a = -3.16 x 1014 m/s2 t = 1.4 x 10-8 sec -3 nC q1 3m 5 cm E1 +6 nC • + q2 E2 A 4 m Signs of the charges are used only to find direction of E -3 nC q1 3m E1 5m +6 nC + q2 • E2 A 4 m E1 E R = E 2 + E1 ; tan φ = E2 2 2 ER φ E2 E1 ER E2 φ E1 E1 = 3.00 N/C, North E2 = 3.38 N/ C, West N 2 N 2 N E = ((3.00 ) + (3.38 ) ) = 4.52 C C C N 3.00 C tan φ = N 3.38 C Resultant Field: ER = 4.52 N/C; 138.40 €