Transcript
Electric Field – Introduction An electric field is said to exist in the region of space around a charged object This charged object is the source charge When another charged object, the test charge, enters this electric field, an electric force acts on it The electric field is defined as the electric force on the test charge per unit charge The electric field vector, , at a point in space is defined as the electric force acting on a positive test charge, qo placed at that point divided by the test charge: More About Electric Field Direction a) q is positive, the force is directed away from q b) The direction of the field is also away from the positive source charge c) q is negative, the force is directed toward q d) The field is also toward the negative source charge Use the active figure to change the position of point P and observe the electric field PLAY ACTIVE FIGURE Find the electric field due to q1, Find the electric field due to q2, Remember, the fields add as vectors The direction of the individual fields is the direction of the force on a positive test charge Superposition with Electric Fields Electric Field Lines Field lines give us a means of representing the electric field pictorially The electric field vector is tangent to the electric field line at each point The line has a direction that is the same as that of the electric field vector The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region Electric Field Lines, General The density of lines through surface A is greater than through surface B The magnitude of the electric field is greater on surface A than B The lines at different locations point in different directions This indicates the field is nonuniform Electric Field Lines The field lines radiate outward in all directions In three dimensions, the distribution is spherical The lines are directed away from the source charge A positive test charge would be repelled away from the positive source charge The field lines radiate inward in all directions The lines are directed toward the source charge A positive test charge would be attracted toward the negative source charge Electric Field Lines The charges are equal and opposite The number of field lines leaving the positive charge equals the number of lines terminating on the negative charge The charges are equal and positive The same number of lines leave each charge since they are equal in magnitude At a great distance, the field is approximately equal to that of a single charge of 2q Electric Field Lines, Unequal Charges The positive charge is twice the magnitude of the negative charge Two lines leave the positive charge for each line that terminates on the negative charge At a great distance, the field would be approximately the same as that due to a single charge of +q Use the active figure to vary the charges and positions and observe the resulting electric field PLAY ACTIVE FIGURE Electric Field Lines – Rules for Drawing The lines must begin on a positive charge and terminate on a negative charge In the case of an excess of one type of charge, some lines will begin or end infinitely far away The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge No two field lines can cross Remember field lines are not material objects, they are a pictorial representation used to qualitatively describe the electric field Motion of Charged Particles When a charged particle is placed in an electric field, it experiences an electrical force If this is the only force on the particle, it must be the net force The net force will cause the particle to accelerate according to Newton’s second law If is uniform, then the acceleration is constant If the particle has a positive charge, its acceleration is in the direction of the field If the particle has a negative charge, its acceleration is in the direction opposite the electric field Since the acceleration is constant, the kinematic equations can be used PLAY ACTIVE FIGURE Electron in a Uniform Field, Example The electron is projected horizontally into a uniform electric field The electron undergoes a downward acceleration It is negative, so the acceleration is opposite the direction of the field Its motion is parabolic while between the plates Use the active figure to vary the field and the characteristics of the particle. PLAY ACTIVE FIGURE Example 23.9 – A uniform electric field of magnitude E is directed along the x axis between the parallel plates separated by a distance d. A positive point particle of charge q is released from point A next to the positive plate, what is the speed with which it strikes the opposite plate? Example 23.10 – An electron enters the region of a uniform electric field of magnitude E=200 N/C with a speed of v= 3.00×106 m/s directed along the x axis between the parallel plates of length l. (a) What is the acceleration of the electron, (b) how long does it take to cross the field region? (c) How far vertically did the electron travel? CHAPTER 25 Objectives Electric Potential Energy Electric Potential WORK DONE BY A FORCE However this mathematical expression only applies under special conditions: constant force throughout the displacement and zero angle between the directions of the force and the displacement. If the angle between the directions of the force and displacement is q but the force is still constant then the work done is given by If either the force or the angle between the directions of the force and displacement is not constant then the work done is given by the general mathematical expression When as a result of the action of a force on a body, the body is displaced we say that the force did work on the body and often use the expression - + + + + + + + + + + - - - - - - - - - - - X A X B d Electrical Potential Energy When a test charge is placed in an electric field, it experiences a force If the test charge is moved in the field by some external agent, the work done by the field is the negative of the work done by the external agent (situation is analogues to lifting an object with mass m in a gravitational field: the work done by the external field is mgh whereas work done by the field is –mgh.) The work done by the electric field is is an infinitesimal displacement vector As this work is done by the field, the potential energy of the charge-field system is changed by ?U = For a finite displacement of the charge from A to B, - + + + + + + + + + + - - - - - - - - - - - X A X B d WORK DONE BY A CONSTANT ELECTRIC FIELD FORCE Then the work done by the electric field force In displacing a charge q from A to B is Let q be the angle that the direction of the field makes with the line that joins the points A and B and l the distance between the two points. Since - + + + + + + + + + + - - - - - - - - - - - X A X B d Potential difference in a uniform electric field DEFINITION: The potential difference between points A and B is given in general by For a uniform electric field The potential difference between points A and B is given by Point A of coordinates (2, 3) m and point B of coordinates (5, 7) m are in a region where the electric field is uniform and given by E = (4i + 3j) N/C. What is the potential difference VA-VB? 33 V 27 V -24 V -27 V +24 V A charged particle (q = –8.0 mC), which moves in a region where the only force acting on the particle is an electric force, is released from rest at point A. At point B the kinetic energy of the particle is equal to 4.8 J. What is the electric potential difference VB-VA? -0.60 kV +0.60 kV -0.80 kV +0.80 kV -0.48 kV A particle (mass = 6.7 ? 10–27 kg, charge = 3.2 ? 10–19 C) moves along the positive x axis with a speed of 4.8 ? 105 m/s. It enters a region of uniform electric field parallel to its motion and comes to rest after moving 2.0 m into the field. What is the magnitude of the electric field? 2.0 kN/C 1.5 kN/C 3.5 kN/C 1.2 kN/C 2.4 kN/C Measurement Units 1 V = 1 J/C V is a volt It takes one joule of work to move a 1-coulomb charge through a potential difference of 1 volt 1 N/C = 1 V/m This indicates we can interpret the electric field as a measure of the rate of change with position of the electric potential Since another unit of energy that is commonly used in atomic and nuclear physics is the electron-volt. One electron-volt is defined as the energy a charge-field system gains or loses when a charge of magnitude e (an electron or a proton) is moved through a potential difference of 1 volt 1 eV = 1.60 × 10-19 J W=qV V=W/q F=Eq E=F/q Energy and the Direction of Electric Field When the electric field is directed downward, point B is at a lower potential than point A When a positive test charge moves from A to B, the charge-field system loses potential energy Use the active figure to compare the motion in the electric field to the motion in a gravitational field Potential and Point Charges A positive point charge produces a field directed radially outward The potential difference between points A and B will be Potential and Point Charges, cont. The electric potential is independent of the path between points A and B It is customary to choose a reference potential of V = 0 at rA = ? Then the potential at some point r is Electric Potential of a Point Charge The electric potential in the plane around a single point charge is shown The red line shows the 1/r nature of the potential Electric Potential with Multiple Charges The electric potential due to several point charges is the sum of the potentials due to each individual charge This is another example of the superposition principle The sum is the algebraic sum V = 0 at r = ? Electric Potential of a Dipole The graph shows the potential (y-axis) of an electric dipole The steep slope between the charges represents the strong electric field in this region Potential Energy of Multiple Charges Consider two charged particles The potential energy of the system is Use the active figure to move the charge and see the effect on the potential energy of the system PLAY ACTIVE FIGURE More About U of Multiple Charges If the two charges are the same sign, U is positive and work must be done to bring the charges together If the two charges have opposite signs, U is negative and work is done to keep the charges apart U with Multiple Charges, final If there are more than two charges, then find U for each pair of charges and add them For three charges: The result is independent of the order of the charges Millikan Oil-Drop Experiment – Experimental Set-Up PLAY ACTIVE FIGURE Millikan Oil-Drop Experiment Robert Millikan measured e, the magnitude of the elementary charge on the electron He also demonstrated the quantized nature of this charge Oil droplets pass through a small hole and are illuminated by a light Oil-Drop Experiment, 2 With no electric field between the plates, the gravitational force and the drag force (viscous) act on the electron The drop reaches terminal velocity with Oil-Drop Experiment, 3 When an electric field is set up between the plates The upper plate has a higher potential The drop reaches a new terminal velocity when the electrical force equals the sum of the drag force and gravity
