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Electric potential, Systems of charges

Explore key concepts of electric potential and energy in systems of charges, including equipotentials and electronvolt. Learn about positive and negative charges in electric fields, potential energy, and superposition of fields. Understand the significance of equipotentials, symmetry in charge distribution, and coordinate systems in simplifying calculations.

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Electric potential, Systems of charges

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  1. Electric potential,Systems of charges Physics 122 Lecture V

  2. Concepts • Primary concepts: • Electric potential • Electric energy • Secondary concepts: • Equipotentials • Electonvolt Lecture V

  3. Charges in electric fields Positive charges experience force along the direction of the field Negative charges – against the direction of the field. + - Lecture V

  4. Potential electric energy High PE High PE Low PE Just like gravity electric force can do work work does not depend on the path it depends only on the initial and final position  there is a potential energy associated with electric field. Low PE Lecture V

  5. Electric potential • PE/q is a property of the field itself – called electric potentialV Lecture V

  6. Electric potential • V – electric potential is the potential energy of a positive test charge in electric field, divided by the magnitude of this charge q. • Electric potential is a scalar (so much nicer!). • Electric potential is measured in Volts (V=J/C). • Potential difference between two points DV=Vb-Va is often called voltage. Lecture V

  7. Charges in electric fields b E=const Force on charge q: F=qE Work done by the field to move this charge W=Fd=dqE W=PEa-PEb=qVa-qVb=-qDV • d E=-DV • E= -DV/d, points from high potential to low • Sometimes electric field is measured in V/m =N/C + a Lecture V

  8. Non-uniform electric field + Lecture V

  9. Electric field and potential in conductors E=0 in good conductors in the static situation. E is perpendicular to the surface of conductor. Metal hollow boxes are used to shield electric fields. When charges are not moving conductor is entirely at the same potential. + + + + + - - - - - Lecture V

  10. Electronvolt • Energy that one electron gains when being accelerated over 1V potential difference is called electronvolt eV: • 1eV=1.6x10-19C 1V= 1.6x10-19J • Yet another unit to measure energy, • Commonly used in atomic and particle physics. Lecture V

  11. Equipontentials Equipotentials • are surfaces at the same potential; • are always perpendicular to field lines; • Never cross; • Their density represents the strength of the electric field • Potential is higher at points closer to positive charge Lecture V

  12. Potential of a point charge Potential V of electric field created by a point charge Q at a radius r is Q>0  V>0 Q<0  V<0 Do not forget the signs! Potential goes to 0 at infinity. Equipotentials of a point charge are concentric spheres. + Lecture V

  13. Superposition of fields Principle of superposition: Net potential created by a system of charges is a scalar (!) sum of potentials created by individual charges: + + - 1 2 Potential is a scalar  no direction to worry about. Lecture V

  14. Electric Dipole potential -Q +Q l P • evaluate potential at point P r+D r r • for r >> L, D r=lcosq q Lecture V

  15. Test problem • What is wrong with this picture? • A Equipotentials must be parallel to field lines • B Field lines cannot go to infinity • C Some field lines point away from the negative charge • D Equipotentials cannot be closed Lecture V

  16. Systems of charges Lecture V

  17. The electric potential of a system of charges + + - + + + - + - - - Bunch of Charges Charge Distribution + + + + + + + + + + + Lecture V

  18. Symmetry and coordinate systems • Coordinate systems are there to help you • You have a choice of • System type • Cartesian • Cylindrical • Spherical • Origin (0,0), Direction of axis • A good choice (respecting the symmetry of the system) can help to simplify the calculations Lecture V

  19. Ring of charge • A thing ring of radius a holds a total charge Q. Determine the electric field on its axis, a distance x from its center. a x q Lecture V

  20. Ring of charge • A thing ring of radius a holds a total charge Q. Determine the electric potential on its axis, a distance x from its center. a x Lecture V

  21. Work to move a charge How much work has to be done by an external force to move a charge q=+1.5 mC from point a to point b? Work-energy principle + 30cm + 20cm 15cm 25cm + - Q1=10mC Q2=-20mC Lecture V

  22. Determine E from V • Think ski slopes • If V depends on one coordinate x • E is directed along x from high V to low • If V depends on x,y,z Lecture V

  23. E near metal sphere • Find the largest charge Q that a conductive sphere radius r=1cm can hold. • Air breakdown E=3x106V/m Larger spheres can hold more charge Lecture V

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