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Transcript
Electric Field Define the concept of a field A field is an area or volume that has a number, representing some quantity, assigned to every location. That number can be a scalar or a vector. A football field has numbers assigned in one dimension A weather map is an example of a scalar field. Every point on the map has a scalar quantity associated with it. In this case, it’s temperature. For example, the temperature in NP is about 75o Vector Field Examples - Has an amount and a direction associated with each position. “Action at a distance” • The electric force is another force that is able to act at a distance. (Just like gravity) • Electric charges don’t need to be touching to exert a force on each other. • This means the electric force must be a field force. Electric Field • All charges create an electric field around themselves. • Any other charge in that electric field will experience an electric force & will either be attracted or repelled by the original charge. • It is this electric field that extends out around a charge that allows that charge to act at a distance on another charge. This is similar to a gravitational field. Any object near the surface of the Earth will accelerate towards the Earth at 9.8 m/s2 Any object that is 3.8x108 m from the surface of the Earth will accelerate towards the Earth at 0.00272 m/s2 Only charges are more complicated. • Masses only attract so all gravitational fields point towards the mass creating them. • Charges can both attract and repel. So the field might point towards a charge or away from the charge creating the field, depending on its charge. Test Charge • To determine the direction of the electric field, a test charge is used. • A test charge is a pretend positive point charge that is infinitely small and has a very very small positive charge so it will not disrupt the field it is in at all. • The test charge is always positive, never negative. Draw the electric field around a positive charge. Electric field for a positive charge + Draw the electric field for a negative charge. Drawing Electric Field Lines 1. The lines must begin on positive charges and end on negative charges, or at infinity. 2. The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the amount of charge. 3. Field lines may not cross or touch each other. This implies that the vector sum has two values---which it can’t 4. Field lines must meet conductors or charges perpendicular to the surface of the conductor or charge. Example: 2 Charges Example: Charge & Plate This is an equipotential line. Do not worry about it for now. Back to Earth’s Gravitational Field: Mass CREATING Near the surface of the Earth, Earth’s gravitational the fieldfield is 9.8 N/kg downwards, toward Earth’s surface. Mass EXPERIENCING Do larger masses experience a larger gravitational field the field from Earth? What two variables does gravitational field depend on? æ GM 2 ö GM1M 2 Fg = = M1 ç 2 ÷ = mg 2 è R ø R Calculation of a Gravitational Field (on Earth 9.8 m/s2) It is the same thing with electric fields This charge EXPERIENCES the field kQ1Q2 F 2 d This charge CREATES According to Coulomb’s Law: kQ F 2 Q d the field This part of Coulomb’s Law calculates the Electric Field (E) The electric field produced by a point or spherical charge is given by…. The direction of the kQ E 2 d electric field is based on the direction of force for a positive charge. K = Coulomb’s Constant (9.0x109 N m2/C2) Q = The charge producing the field. Coulombs Given in d = The distance to the point in question Q Another way to calculate electric force is this: This charge EXPERIENCES the field kQ1Q2 F 2 d This charge CREATES According to Coulomb’s Law: kQ F 2 Q d the field Another way to calculate electric force is this: F EQ E (electric field) Another way to calculate electric force: F EQ • F = Electric Force (N) • E = Electric Field (N/C) • Q = Charge placed in the electric field (C) Very similar to Fg = mg What is the electric field 20.00 m to the right of a (+) 0.0025 C point charge? + .0025 C 20.00 m E=? kQ E 2 d 9.0 ´10 9 (.0025C ) E= 2 2 20.00 m = 5.6x104 N/C Two charges are along the x-axis. Q1 is 3.0 m from the origin and has a charge of -12.0mC. Q2 is 4.5 m from the origin and has a charge of +4.0mC. (all charges are along the positive x-axis) a) Calculate the electric field 8.0 m from the origin. 0.0 m kQ1 E1 = 2 d1 3.0 m 4.5 m 8.0 m - + E=? Q1 = - 12.0x10-6C -6 (9 ´10 )(-12.0 ´10 ) E1 = 5.0 2 9 E1 = 4320N / C kQ2 E2 = 2 d2 (9 ´10 9 )(+4.0 ´10-6 ) E2 = 3.52 Q2 = + 4.0x10-6C E2 = 2939N / C 0.0 m 4.5 m 3.0 m + Q1 = - 12.0x10-6C Q2 = + 4.0x10-6C E1 = 4320N / C E2 = 2939N / C = ETotal =1400N / C 8.0 m E=? b) What force will a - 9.0 mC charge experience if it is placed 8.0 m from the origin? 0.0 m 3.0 m 4.5 m - + Q1 = - 12.0x10-6C Q2 = + 4.0x10-6C 8.0 m Q3 = - 9.0x10-6C E = 1381 N/C F = QE F = (-9.0x10-6C)(1380N/C) F = 0.012 N Two charges, +Q and –Q, are located two meters apart as shown. Which vector best represents the direction of the electric field at the point above them? 2 3 1 4 + - Two charges, +Q and –Q, are located two meters apart as shown. Which vector best represents the direction of the electric field at the point above them? 3 + - Two point charges, separated by 1.5cm, have charges of +2 and -4C. Suppose we determine that 10 field lines radiate out from the +2C charge. If so, what might be inferred about the -4C charge with respect to field lines? 1) 20 radiate out 4) 10 radiate in 2) 5 radiate out 5) 5 radiate in 3) 20 radiate in