Electricity -1. q p = C. q e

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1 Electricity -1 The Electric Charge: As far as electricity concerned there are three kinds of particles: negatively electric charged particles (like electron) positively charged particles (like proton) neutral particles (like neutron) The electric charge is measured in a natural unit called e, or in a unit called Coulomb (C). e = C. The charge of the electron is q e = e = C, the charge of the proton is q p = e = C, and the charge of a neutron is 0, i.e it has no electric charge. Examples: 1. How many electrons are there in a -10C charge? 2. How many protons are there in a 10C charge? 3. How many neutrons are there in a 5C charge? The electric charge is a conserved quantity. That is the net electric charge in a closed system always stays the same. The charge of an object always can be written as a multiple of the charge of the electron or the proton. The Electric Force: Electrically charged particles experience the electric force. Unlike the gravitational force--which is always attractive, the electric force between two objects can be repulsive or attractive, or zero. The electric force between like charges is repulsive while the electric force between unlike charges is attractive. Any time you are in doubt, remember that the hydrogen atom is made of one electron and one proton Since the H-atom does not disintegrate by itself, the force between the proton and the electron must be attractive. In orbital motion the net force is always attractive. In the case of the H-atom, it is the electric force that keeps the electron on its orbit. The Electric Field: Any object with electric charge produces an electric field the way any object with mass produces a gravitational field. However, unlike gravitational field--which is always attractive in the radially inward direction, the electric field can be inward or outward. Flux: The flux of a vector field is a measure of the flow of the vector field through an area. The flux of the electric field: Φ E = E r A r Gauss Law: Const Source=Field Area For E-field with a point charge: Const=4πk, Source=Q, Field=E, Area=4πr 2 Problems: Use Gauss Law to derive an expression for the electric field produced by 1. a point charge 2. a chargeplane (very large) 3. a charged line (very long) Questions: 1. What holds a galaxy together; what about a star, a planet? 2. What holds an object together; what about a person, a plant? 3. What (force) is the cause of friction? Comparison of Gravitation and Electricity Source Mass, M Charge, q Constant G = N m 2 k g 2 k = N m 2 Force Field Force g = G M r 2 ( r) F G = G M 1 M 2 r 2 ( r ) C 2 E = k q r 2 ( r ) F E = k q 1q 2 r 2 ( r ) where r shows the radially outward direction and r shows the radially inward direction. Some constants (order of magnitude values): m p = kg m n = kg m e = kg m H = kg G = N m2 k g 2 The gravitational field of an object is always towards the object The gravitational force between two masses is always attractive q p = C q n = 0 q e = C q H = 0 k = N C2 k g 2 The electric field of a negative charge is inward The electric field of a positive charge is outward The electric force between two unlike charges is attractive, between two like charges is repulsive r p = m r n = m r e = 0 r H = m

2 Examples: 1. Obtain the electric field E caused by the proton at a distance r H = m. Compare it to the gravitational field caused by the proton at that distance. Electricity -2 Electric Potential Energy PE E = k q 1q 2 R 1,2 1. Obtain the electric potential energy of the electron due to the proton in the hydrogen atom. 2. Obtain the electric field E caused by the electron at a distance r H = m. Compare it to the gravitational field caused by the electron at that distance. 2. Obtain the electric potential energy of the proton due to the electron in a hydrogen atom. 3. Obtain the escape velocity of the electron in the hydrogen atom. 3 Obtain the electric field E caused by the neutron at a distance r H = m. Compare it to the gravitational field caused by the neutron at that distance. 4. Obtain the electric force caused by the proton on the electron in the hydrogen atom. Compare it to the gravitational force caused by the proton on the electron. 4. Obtain the escape velocity of the proton in the hydrogen atom. 5. a. Assume that the whole earth is made of protons only. Use the mass of the earth and the mass of the proton to calculate the approximate number of protons in the earth. b. Next assume that your body consists of only protons. Calculate the approximate number of protons in your body. 5. Obtain the electric force caused by the electron on the proton in the hydrogen atom. Compare it to the gravitational force caused by the electron on the proton. c. Calculate the electric force between your body and the earth under the conditions of parts and b. How many times is this force stronger than the gravitational force between you and your body? Could you survive under these conditions? 6. Obtain the electric force between the electron and the proton in the hydrogen atom. Compare it to the gravitational force between the electron and the proton. 7. How are your answers to 4, 5, and 6 related? Why? Which force is larger? How many times? Which force do you think is responsible for holding the hydrogen atom together, gravitational or electrical? 8. Use your answer to question 7 as the source of the centripetal force and calculate the approximate velocity of the electron on its orbit around the proton. d. What do your think prevents the electric force to be this strong between you and the earth? 6. Use conservation of energy to obtain the escape velocity of the electron from the proton in the hydrogen atom. Inside the hydrogen atom: E = 1 2 M e v2 k q pq e At infinity: As a result E= M e v2 = k q pq e R H v E = 2 k q p q e M e R H R H

3 Electricity -3 Problems 1. For the set up below, calculate the net electric field at the locations of a. 10 C charge b. 20 C charge c. 30 C charge d. Calculate the net force acting on each charge (Give yoour answers in mks units.) 2. For the set up below, calculate the net electric field at the locations of a. 10 C charge b. 20 C charge c. 30 C charge d. Calculate the net force acting on each charge (Give yoour answers in mks units.) 10 C p 3. For the figure shown obtain 1m a. Enet where the lower left hand corner e - electron is. b. Fnet on the lower left hand corner electron c. Enet at the center d. Fnet at the center. 50 cm 100 cm 10 C 20 C 25 cm 20 C 100 cm e - 1m 1m 30 C 30 C 1m p Hints: 1. a. In calculating the electric field at the location of the 10C charge, we ignore the 10 C charge itself. i. Be consistent with the use of units ii. Obtain the electric field caused by the -20 C charge at that location (do not forget to figure out its direction!) iii. Obtain the electric field caused by the 30 C charge at that location (do not forget to figure out its direction!) iv. Obtain the net electric field by obtaining the vectorial sums of the two electric fields. Repeat these steps for parts b & c. In part b ignore the - 20 C charge, in part c ignore the 30 C charge. To obtain the net force acting on each charge, repeat the steps above for each charge or use F=qE. 2. a. To obtain the net electric field at the location of the 10 C charge, calculate i. the electric field caused by the -20 C charge at that location ii. the electric field caused by the 30 C charge at that location iii. the vectorial sum ot the two fields Toobtain the net force on the -20 C charge, use F=qE or follow the steps above for the forces. 2. b. To obtain the net electric field at the location of the -20 C, we need to i. know all the distances. Use the Pythagorian theorem to calculate the distance between -20 C and 30 C ii. know the directions o the electric field caused by the 10 C charge at that location ii. the electric field caused by the 30 C charge at that location iii. the vectorial sum ot the two fields Toobtain the net force on the -20 C charge, use F=qE or follow the steps above for the forces. 4. For the figure shown obtain a. Enet where the lower left hand corner proton is. b. Fnet on the lower left hand corner proton c. Enet at the center d. Fnet at the center. p 1m e - 1m 1m p 1m e-

4 Electricity -4 Work done by the Electric Force: The general expression for the work done on an object is given by W net = F net d = F net d cos θ where d is the distance covered by the object under the effect of the force. In the case of electricity, the force acting on a charge object is F net = q E net. As a result, W net = F net d = q E net d cos θ E x a m p l e : 1. A particle of charge 10 C moves 10 m under the effect of an electric field of strength 10 N C. Obtain the work done by the electric field if the particle moves a. along the electric field b. against the electric field c. at a 30 angle with respect to the E-field d. at a 60 angle with respect to the E-field. Electric Potential: Electric potential is the electric potential energy per unit charge. This is also called Voltage. V = PE q 2. A particle of charge 20 C has 100J of potential energy. Obtain the electric potential (voltage). 3. What would be the potential energy of an electron if it is in a region where the voltage is 40 V with respect to ground? 4. How would your answer to example 3 change if the particle is a. a proton b. a neutron c. a neutral hydrogen atom d. ionized hydrogen atom (H, or H - ) Electric potential difference between two points is given by V 2,1 = V 2 V 1 = PE 2 q PE 1 q In other words a particle of charge q experiences an electric potential energy difference of q V 2,1 = PE 2 PE 1 these two points. If there is a voltage difference V 2,1 between two points, a particle of charge q moves towards the lower voltage and experiences a change in its kinetic energy. In other words, q V 2,1 = PE 2 PE 1 = KE 1 KE 2 This is similar to an object s motion under the effect of gravity. In the case of gravity Mgh 2 Mgh 1 = KE 1 KE 2 A positive charge moves from the higher voltage to the lower voltage, and a negative charge moves from the lower voltage to the higher voltage, 5. A particle moves from point 1 where the voltage is -20 V to point 2 where the voltage is 20 V. Obtain the voltage difference between the two points. What will be the change in the electric potential energy of this particle if the particle is a. an electron b. a proton c. a neutron 6. How much would the kinetic energy of the particle in example 5 change in moving from point 1 to point 2. a. an electron b. a proton c. a neutron 7. If in example 5 the initial velocity of the particle at point 1 is 10 m s, obtain its velocity at point 2. a. an electron b. a proton c. a neutron

5 Electricity -5 Problem: Consider the set up below. The magnitude of the electric field inside the plates is 100N/C. a. What is the direction of the electric field inside the plates? Why? b. Obtain the electric potential difference between the plates. c. If the following particles are put where the circle is, in what direction would they go? Ignore Earth s gravity. electron proton neutron 2m 5m 3m d. An electron is put where the circle is with zero initial velocity. How much work will the electricity do in moving the electron towards the plate that the electron is attracted? e. What will be the electron s kinetic energy when it reaches this plate? f. With what velocity will the electron hit the plate? Electric Potential (Voltage): Electric Potential Energy per unit charge Electric Current: The flow electric charge per unit time Resistor: Electric element that resists the flow of electric charge Capacitor: A device to store electric charge, thus potential. Capacitor Problems: 1. What does an ideal capacitor behave like? 2. Use an order of magnitude calculation to derive an expression for thecapacitance of a. a parallel-plate capacitor b. a spherical capacitor c. a cylindrical capacitor 3. Use the definiton for capacitance C = Q to derive ΔV the capacitance expressions of the capacitors in the preceding question. 4. How would a dielectric affect the capacitance of a capacitor? Increase or decrease it? 5. Use the properties of the voltage across and the charge on a capacitor to derive an expression for the equivalent capacitance of capacitors connected in a. series b. parallel Resistor Problems: 1. What does an ideal resistor behave like? 2. Use an order of magnitude calculation to derive an expression for reistance of a cylindrical wire. 3. Use the properties of the voltage across and the current through a resistor to derive an expression for the equivalent resistance of resistors connected in a. series b. parallel Power consmed by a resistor: DC-Circuits Equivalent resistance, capacitance, etc. Kirchhoff s Rules Junction Rule: Conservation of Charge Loop Rule: Conservation of Energy

6 Electricity -6 Circuit Problems: 1. For the circuit below, 2µF V 1µF 3µF A. Calculate the voltage across, the charge on, energy stored in each capacitor. B. How much charge and energy are there in the circuit? C. Do your answers to A and B agree. In other words, is the sum in A equal to answer in B? 2. For the circuit below, V 2 Ω 1 Ω 3 Ω A. Calculate the voltage across, the current through, and power consumedby each resistor. B. How much current leaves the voltage source and how much power is produced by the battery? C. Do your answers to A and B agree. In other words, is the sum in A equal to answer in B?