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Electric Field

q 1. q 2. r. Electric Field. 1,2. 1,2. 1,2. Question : Why q1 can feel q2 without direct contact?. just as air around us, there’re something around a charge, i.e. electric field (photons) that transfer the force.

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Electric Field

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  1. q1 q2 r Electric Field 1,2 1,2 1,2 Question: Why q1 can feel q2 without direct contact? • just as air around us, there’re something around a charge, i.e. electric field (photons) that transfer the force.

  2. Defineelectric field, which is independent of the test charge, q, and depends only on position in space: Electric Field q F Q Electric Field due to a Point Charge Q • Direction of Electric Field • point away from positive charges • Point to negative charges.

  3. 72 73 77 75 71 82 77 84 68 80 64 73 83 56 55 57 66 88 80 75 88 90 83 92 91 Electric Field With this concept, we can “map” the electric field anywhere in space produced by any arbitrary charge: a Vector field

  4. Electric Field due to Multiple Point Charges The force on a test charge is then given by F1 + + + + F2 so the electric field is, by definition, given by F3 q0 Principle of Superposition!

  5. Both charges > 0 • One is > 0, the other < 0 -q q electric dipole of dipole moment: if |qR|>|qL| if |qL|>|qR| Example: Two charges of the same magnitude x

  6. A visualization tool to illustrate the geometry of an electric field. Electric field lines originate from positive charges and terminates at negative charges. The direction of the electric field at any location is tangential to the field line there. The magnitude of the electric field at any location is proportional to the density of the lines there. # lines/area ~ 1/r2 ~ |E| Electric Field Lines (or at infinity)

  7. Electric field lines of two charges of equal magnitude dipole • Field lines do NOT cross • They do NOT come out of nowhere or vanish into a point. Far from the charges, electric field lines resemble those of a point charge.

  8. Electric field lines of two charges Far from charges, the field lines are as if they are due to a point charge of +2q-q=+q # lines proportional to the magnitude of charge http://www.its.caltech.edu/~phys1/java/phys1/EField/EField.html http://www.falstad.com/vector3de/

  9. Warm-up quiz What is the direction of the electric field at the center of the two point charges? (Take Q > 0.) toward the lower right toward the upper left upward to the right none of the above -Q Q

  10. Electrostatic force on the charge q due to E: E acting on the charge is produced by the other charges (external field). Dimension of E = [force]/[charge] and its SI units = N/C Work done by E on q in moving the charge: Point Charge in an Electric Field F is parallel to E ifthe charge is positive and anti-parallel if the charge is negative The charge is not affected by its own electric field. W is path( )-independent => Conservative force

  11. Dynamics of a Charge in Electric Field For -Q<0 in uniformEdownward: -Q • Oscilloscope • Ink-Jet Printing • Oil drop experiment http://canu.ucalgary.ca/map/content/force/elcrmagn/simulate/electric_single_particle/applet.html

  12. Electric Field due to an Electric Dipole At point P on z-axis: Where is the (magnitude of) dipole moment.

  13. Dipole Field Anisotropy z y At point P on y-axis: Dipole Field at General Point P: where is the unit vector from the center of dipole to the observation point P.

  14. Electric Dipoles • Typical dipole consists of positive and negative charges slightly displaced. • General definition of dipole moments exists: • Water molecule can be thought of as consisting of 2 standard dipoles at an angle to each other. • Net neutral molecules can have electrical dipole moments • Permanent dipole moment (polar) vs. induced dipole moment

  15. Dipole in uniform electric fields • No net force.The electrostatic forces on the constituent point charges are of the same magnitude but along opposite directions. So, there is no net force on the dipole and thus its center of mass should not accelerate. • Net torque!There is clearly a net • torque acting on the dipole with respect to its center of mass, since the forces are not aligned. Clockwise about the center of mass http://qbx6.ltu.edu/s_schneider/physlets/main/dipole_torque.shtml

  16. F x q CM F Torque on the Dipole The magnitude of the torque: The torque points into the screen.

  17. Physics 241 – Sample Quiz A – January 9, 2008 Four point charges are arranged at the corners of a square as shown. What is the direction of the electric field at the center of the square? (Take Q > 0.) toward the lower right toward the upper left upward to the right none of the above -Q - Q Q Q

  18. Physics 241 – Sample Quiz B – January 9, 2008 Four point charges are arranged at the corners of a square as shown. What is the direction of the electric field at the center of the square? (Take Q > 0.) toward the lower right toward the upper left upward to the right none of the above Q - Q Q Q

  19. Physics 241 – Sample Quiz C – January 9, 2008 Three point charges are arranged at three of the corners of a square as shown. What is the direction of the electric field at the center of the square? (Take Q > 0.) toward the lower right toward the upper left upward to the right none of the above Q Q Q

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