Electric Fields Review of gravitational fields Electric field vector Electric fi
Davison, Sydney, Founding Editor has reference to this Academic Journal, PHwiki organized this Journal Electric Fields Review of gravitational fields Electric field vector Electric fields as long as various charge configurations Field strengths as long as point charges in addition to uni as long as m fields Work done by fields & change in potential energy Potential & equipotential surfaces Capacitors, capacitance, & voltage drops across capacitors Millikan oil drop experiment Excess Charge Distribution on a Conductor Gravitational Fields: Review Recall that surrounding any object with mass, or collection of objects with mass, is a gravitational field. Any mass placed in a gravitational field will experience a gravitational as long as ce. We defined the field strength as the gravitational as long as ce per unit mass on any test mass placed in the field: g = F / m. g is a vector that points in the direction of the net gravitational as long as ce; its units are N / kg. F is the vector as long as ce on the test mass, in addition to m is the test mass, a scalar. g in addition to F are always parallel. The strength of the field is independent of the test mass. For example, near Earths surface mg / m = g = 9.8 N / kg as long as any mass. Some fields are uni as long as m (parallel, equally spaced fields lines). Nonuni as long as m fields are stronger where the field lines are closer together. 98 N m F uni as long as m field nonuni as long as m field Electric Fields: Intro Surrounding any object with charge, or collection of objects with charge, is a electric field. Any charge placed in an electric field will experience a electrical as long as ce. We defined the field strength as the electric as long as ce per unit charge on any test charge placed in the field: E = F / q. E is a vector that points, by definition, in the direction of the net electric as long as ce on a positive charge; its units are N / C. F is the vector as long as ce on the test charge, in addition to q is the test charge, a scalar. E in addition to F are only parallel if the test charge is positive. Some fields are uni as long as m (parallel, equally spaced fields lines) such as the field on the left as long as med by a sheet of negative charge. Nonuni as long as m fields are stronger where the field lines are closer together, such as the field on the right produced by a sphere of negative charge. – – – – – – – – – – – – – – q F q F uni as long as m field nonuni as long as m field + +
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Overview of Fields Charge, like mass, is an intrinsic property of an object. Charges produce electric fields that affect other charges; masses produce gravitational fields that affect other masses. Gravitational fields lines always point toward an isolated mass. Unlike mass, though, charges can be positive or negative. Electric field lines emanate from positive charges in addition to penetrate into negative charge. We refer to the charge producing a field as a field charge. A group of field charges can produce very nonuni as long as m fields. To determine the strength of the field at a particular point, we place a small, positive test charge in the field. We then measure the electric as long as ce on it in addition to divide by the test charge: For an isolated positive field charge, the field lines point away from the field charge (since the as long as ce on a positive charge would be away from the field charge). The opposite is true as long as an isolated negative field charge. No matter how complex the field, the electric as long as ce on a test charge is always tangent to the field line at that point. The coming slides will reiterate these ideas in addition to provide examples. E = F / q. Electric & Gravitational Fields Compared Gravity: Electric Force: Field strength is given by per unit mass or as long as ce per unit charge, depending on the type of field. Field strength means the magnitude of a field vector. Ex 1: If a +10 C charge is placed in an electric field in addition to experiences a 50 N as long as ce, the field strength at the location of the charge is 5 N/C. The electric field vector is given by: E = 5 N/C, where the direction of this vector is parallel to the as long as ce vector ( in addition to the field lines). Ex 2: If a -10 C charge experiences a 50 N as long as ce, E = 5 N/C in a direction opposite the as long as ce vector (opposite the direction of the field lines). Electric Field Example Problem A sphere of mass 1.3 grams is charged via friction, in addition to in the process excess electrons are rubbed onto it, giving the sphere a charge of – 4.8 C. The sphere is then placed into an external uni as long as m electric field of 6 N/C directed to the right. The sphere is released from rest. What is its displacement after 15 s (Hints on next slide.) E –
Sample Problem Hints q E m g E – Draw a vector as shown. Note that FE = q E, by definition of E, in addition to that FE is to the left (opposite E ) since the charge is negative. Instead of finding the net as long as ce (which would work), compute the acceleration due to each as long as ce separately. 3. Find the displacement due to each as long as ce using the time given in addition to kinematics. 4. Add the displacement vectors to find the net displacement vector. Drawing an E Field as long as a Point Charge + + Lets use the idea of a test charge to produce the E field as long as an isolated positive field charge. We place small, positive test charges in the vicinity of the field in addition to draw the as long as ce vector on each. Note that the closer the test charge is to the field charge, the greater the as long as ce, but all as long as ce vectors are directed radially outward from the field charge. At any point near the field charge, the as long as ce vector points in the direction of the electric field. Thus we have a field that looks like a sea urchin, with field lines radiating outward from the field charge to infinity in all direction, not just in a plane. The number of field lines drawn in arbitrary, but they should be evenly spaced around the field charge. What if the field charge were negative Test charges in addition to as long as ce vectors surrounding a field charge Isolated, positive point charge in addition to its electric field Single Positive Field Charge This is a 2D picture of the field lines that surround a positive field charge that is either point-like or spherically symmetric. Not shown are field lines going out of in addition to into the page. Keep in mind that the field lines radiate outwards because, by definition, an electric field vector points in the direction of the as long as ce on a positive test charge. The nearer you get to the charge, the more uni as long as m in addition to stronger the field. Farther away the field strength gets weaker, as indicated by the field lines becoming more spread out.
Single Negative Field Charge – The field surrounding an isolated, negative point (or spherically symmetric) charge looks just like that of an isolated positive charge except the field lines are directed toward the field charge. This is because, by definition, an electric field vector points in the direction of the as long as ce on a positive test charge, which, in this case is toward the field charge. As be as long as e, the field is stronger where the field lines are closer together, in addition to the as long as ce vector on a test charge is parallel to the field. Point Charges of Different Magnitudes + 1 Lets compare the fields on two separate isolated point charges, one with a charge of +1 unit, the other with a charge of +2 units. It doesnt matter how many field lines we draw emanating from the +1 charge so long as we draw twice as many line coming from the +2 charge. This means, at a given distance, the strength of the E field as long as the +2 charge is twice that as long as the +1 charge. + 2 Equal but Opposite Field Charges Pictured is the electric field produced by two equal but opposite charges. Because the charges are of the same magnitude, the field is symmetric. Note that all the lines that emanate from the positive charge l in addition to on the negative charge. Also pictured is a small positive charge placed in the field in addition to the as long as ce vector on it at that position. This is the vector sum of the as long as ces exerted on the test charge by each field charge. Note that the net as long as ce vector is tangent to the field line. This is always the case. In fact, the field is defined by the direction of net as long as ce vectors on test charges at various places. The net as long as ce on a negative test charge is tangent to the field as well, but it points in the opposite direction of the field. (Continued on next slide.) + Link 1 Link 2 Link 3
Coulombs Law Review The as long as ce that two point charges, Q in addition to q, separated by a distance r, exert on one another is given by: where K = 9 109 Nm2/C2 (constant). This as long as mula only applies to point charges or spherically symmetric charges. Suppose that the as long as ce two point charges are exerting on one another is F. What is the as long as ce when one charge is tripled, the other is doubled, in addition to the distance is cut in half Answer: 24 F Field Strengths: Point Charge; Point Mass Suppose a test charge q is placed in the electric field produced by a point-like field charge Q. From the definition of electric field in addition to Coulombs law K Q q / r 2 E = F q = q K Q r 2 = Note that the field strength is independent of the charge placed in it. Suppose a test mass m is placed in the gravitational field produced by a point-like field mass M. From the definition of gravitational field in addition to Newtons law of universal gravitation G M m / r 2 g = F m = m G M r 2 = Again, the field strength is independent of the mass place in it. Uni as long as m Field – – – – – – – – + + + + + + + + Just as near Earths surface the gravitational field is approximately uni as long as m, the electric field near the surface of a charged sphere is approximately uni as long as m. A common way to produce a uni as long as m E field is with a parallel plate capacitor: two flat, metal, parallel plates, one negative, one positive. Aside from some fringing on the edges, the field is nearly uni as long as m inside. This means everywhere inside the capacitor the field has about the same magnitude in addition to direction. Two positive test charges are depicted along with as long as ce vectors.
More field lines emanate from the greater charge; none of the field lines cross in addition to they all go to infinity. The field lines of the greater charge looks more like that of an isolated charge, since it dominates the smaller charge. If you zoomed out on this picture, i.e., if you looked at the field from a great distance, it would look like that of an isolated point charge due to one combined charge. Two + Field Charges of Different Magnitude Although in this pic the greater charge is depicted as physically bigger, this need not be the case. Opposite Signs, Unequal Charges + – The positive charge has a greater magnitude than the negative charge. Explain why the field is as shown. (Answer on next slide.) Opposite Signs, Unequal Charges (cont.) More field lines come from the positive charge than l in addition to on the negative. Those that dont l in addition to on the negative charge go to infinity. As always, net as long as ce on a test charge is the vector sum of the two as long as ces in addition to its tangent to the field. Since the positive charge has greater magnitude, it dominates the negative charge, as long as cing the turning points of the point to be closer to the negative charge. If you were to zoom out (observe the field from a distance) it would look like that of an isolated, positive point with a charge equal to the net charge of the system. + –
Summary of Fields due to Unequal Charges You should be able to explain each case in some detail. Review of Induction Valence electrons of a conductor are mobile. Thus they can respond to an electric as long as ce from a charged object. This is called charging by induction. Note: not all of the valence electrons will move from the bottom to the top. The greater the positive charge brought near it, in addition to the nearer it is brought, the more electrons that will migrate toward it. (See animation on next slide.) conductor Review of Induction (cont.) Because of the displaced electrons, a charge separation is induced in the conductor.
Fields: Work & Potential Energy Earths surface m m g Negatively charged surface q E +q g E The work your applied as long as ce does on the mass or on the charge can go into kinetic energy, waste heat, or potential energy. If there is no friction in addition to no acceleration, then the work you do goes into a change of potential energy: U = m g h as long as a mass in a gravitational field in addition to U = q E h as long as a charge in a uni as long as m electric field. The sign of h determines the sign of U. (If a charged object is moved in a vicinity where both types of fields are present, wed have to use both as long as mulae.) Whether or not there is friction or acceleration, it is always the case that the work done by the field is the opposite of the change in potential energy: Wfield = – U. Work-Energy Example + + + + + – – – – – + Here the E field is to the right in addition to approximately uni as long as m. The applied as long as ce is FA to the left, as is the displacement. The work done by FA is + FA d. The work done by the field is WF = – q E d. The change in electric potential energy is U = – WF = + q E d. Since FA > q E, the applied as long as ce does more positive work than the field does negative work. The difference goes into kinetic energy in addition to heat. The work done by friction is Wfric < 0. So, Wnet = FA d - q E d - Wfric = K by the work-energy theorem. q FA q E d Work-Energy Practice For each situation a charge is displaced by some applied as long as ce while in a uni as long as m electric field. Determine the sign of: the work done by the applied as long as ce; the work done by the field; in addition to U. 1. q is positive in addition to displaced to the right. + + + + + - - - - - q 2. q is negative in addition to displaced to the right. 4. q is negative in addition to displaced to the left. 3. q is positive in addition to displaced to the left. Credits http://images.google.com/imgresimgurl=http://buphy.bu.edu/~duffy/PY106/2e.GIF&imgrefurl=http://physics.bu.edu/~duffy/PY106/Electricfield.html&h=221&w=370&sz=4&tbnid=y0qny4b133kJ:&tbnh=70&tbnw=117&start=3&prev=/images%3Fq%3Delectric%2Bfield%26hl%3Den%26lr%3D Spark Picture: http://cdcollura.tripod.com/tcspark2.htm electric field lines: http://www.gel.ulaval.ca/~mbusque/elec/main-e.html java, placing in addition to moving test charges in addition to regular charges: http://www.physicslessons.com/exp21b.htm java animation, placing test charges: http://www.colorado.edu/physics/2000/waves-particles/wavpart3.html http://www.slcc.edu/schools/hum-sci/physics/tutor/2220/e-fields/ lesson, pictures, units: http://www.pa.msu.edu/courses/1997spring/PHY232/lectures/efields/ java electric field: http://www.msu.edu/user/brechtjo/physics/eField/eField.html lesson with animations, explanations: http://www.cyberclassrooms.net/~pschweiger/field.html http://library.thinkquest.org/10796/ch12/ch12.htm Robert Millikan: http://www.nobel.se/physics/laureates/1923/millikan-bio.html Millikan Oil Drop: http://www.mdclearhills.ab.ca/millikan/experiment.html
Davison, Sydney Founding Editor
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