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L 30 E G Fields 2 (with Answers).pptx
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Скачать презентацию L 30 — Forces and Fields By the
Скачать презентацию L 30 — Forces and Fields By the
L 30 - Forces and Fields. By the end of the lecture… • Understand, both qualitatively and quantitatively, the relationship between field strength and potential at a point, for electric and gravitational fields • Be able to derive, by integration, the formulae for the potential energy of two particle systems in both electric and gravitational fields • Understand the concepts of potential difference and potential gradient • Know quantitative formulas which define the gravitational potential, electric potential. • Know what an equipotential is • Be able to perform a variety of calculations that demonstrate your understanding
Gravitational Field The force, FG, acting on a unit mass placed at each point in space. The gravitational field, g, due to a point mass
Uneven distribution of Earth’s gravitational field at surface.
Picturing E Field and G Fields • Electric Field lines or “lines of force”. • The tangent to a field line is the direction of the E field at that point. • The flux through an area is the total number of field lines that pass through the area. • The field lines are closer together where the field is greater, i. e. the flux density is greater. • Flux density is the number of lines of force per unit area where the area is perpendicular to the lines.
Field due to point charges − The flux density and therefore the E field obeys inverse square law. − Field lines start on positive charges and end on negative charges. − Field lines can never cross. pos neg
The dipole field
Example 5: Draw the field between two large parallel conducting plates (capacitor). - + + + http: //www. youtube. com/watch? v=DMz 3 Gte. Jf_4
Electric potential A scalar field, not a vector field. Potential difference is work done to move unit charge from one position to another position.
Consider a constant E field region: e. g. , between the plates of a capacitor. ΔV = - E Δx d. V = - E dx giving the equation: E is the negative of the gradient of V Thus, the scalar field V can be used to deduce the vector field E
Visualising a potential field
Example 1: The voltage between the anode and cathode of an electron gun is 2500 V. What is the velocity of the electrons emitted from the gun?
Example 2: A parallel plate capacitor consists of two large plates that are 2. 00 cm apart. The potential difference between the plates is 4. 00 V. A) What is the electric field at a distance of 0. 5 cm from the negative plate? B) If a charge of 50. 0 μC is released at a distance 0. 500 cm from the positive plate, what will be its KE when it arrives at the negative plate?
Electric potential Reference point is at infinity, where potential V = 0. We do work to move a charge q from infinity to a distance r from a point charge Q.
Potential due to a point charge Q Derive the equation
Fields inside good conductor placed in an electric field. E=0 Fields due to a charged sphere
Draw equipotential lines for a point charge + -
For a dipole, where will the equipotential lines be?
Potential Energy and change in Potential Energy PE = q. V Δ PE = q ΔV Example 3: How much work is required to move a charge of +20. 0 μC from a distance of 3. 00 cm to a distance of 7. 00 cm away from a stationary charge of 30. 0 μC?
Example 4: Two points charges, A of 2. 00 n. C and B of -3. 00 n. C are arranged as in the diagram. i) Find the electric potential at P ii) At what distance from A on the line AB is the potential equal to zero?
Gravitational potential and potential energy due to sphere of mass M (e. g. , Earth) Potential energy of mass m near the Earth Change of potential energy in moving upwards to height h =
Example 5: A 300 kg projectile is launched vertically from the Earth’s surface. a) At what speed must the projectile be launched so that it reaches an attitude equal to the radius of the Earth? b) What is its gravitational potential at this attitude? c) What is its gravitational potential energy? Given ME = 5. 97 x 1024 kg RE = 6. 38 x 106 m G = 6. 67 x 10 -11 N m 2 kg -2
Comparison of Electric and Gravitational Fields
Further Reading: Adams and Allday: 5. 3, 5. 4, 5. 8 - 5. 11, 5. 13. Serway: 16. 1 – 16. 4 • Understand, both qualitatively and quantitatively, the relationship between field strength and potential at a point, for electric and gravitational fields • Be able to derive, by integration, the formulae for the potential energy of two particle systems in both electric and gravitational fields • Understand the concepts of potential difference and potential gradient • Know quantitative formulas which define the gravitational potential, electric potential. • Know what an equipotential is • Be able to perform a variety of calculations that demonstrate your understanding
Numerical Answers to Examples 1) 2) 3) 4) 5) V = 2. 96 x 107 m/s a) E = -200 N/C b) KE = 1. 50 x 10 -4 J ∆W = -102 J a) V = -18. 8 Volts b) d = 0. 0800 m (3 sig fig) a) v = 7. 90 x 103 m/s b) VG = 3. 12 x 107 J/kg c) UG = 9. 36 x 108 J
Скачать презентацию L 30 — Forces and Fields By the
L 30 E G Fields 2 (with Answers).pptx