1. Lecture 3-1 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. http://qbx6.ltu.edu/s_schneider/physlets/main/dipole_torque.shtml

2. Lecture 3-2 Torque on the Dipole The magnitude of the torque: The torque points into the screen. x  F F CM

3. Lecture 3-3 Electric Field from Coulomb’s Law + + + + + - - - + - - Bunch of Charges (volume charge) (surface charge) (line charge) Continuous Charge Distribution dq P Summation over discrete charges Integral over continuous charge distribution P k http://www.falstad.com/vector3de/

4. Lecture 3-4 Continuous Charge Distribution 1: Charged Line At a point P on axis:

5. Lecture 3-5 Again: Continuous Charge Distribution 1: Charged Line At a point P on perpendicular axis:  x

6. Lecture 3-6 Physics 241 –Warm-up quiz The rod is uniformly charged with a positive charge density . What is the direction of the electric field at a point P on a line perpendicular to the rod? Note that the line and the rod are in the same plane. a) to the right b) to the left c)  up d) down e) lower right  p

7. Lecture 3-7 General location of P: Charged Line At a point P off axis:

8. Lecture 3-8 Continuous Charge Distribution 2: Charged Ring Use symmetry! At point P on axis of ring: ds 

9. Lecture 3-9 Continuous Charge Distribution 3: Charged Disk <= Independent of x Superposition of rings! At a point P on axis:Use the ring result

10. Lecture 3-10 Continuous Charge Distribution 4: Charged Sheets E=const in each regionSuperposition! Capacitor geometry

11. Lecture 3-11 Physics 241 –Quiz 1A The left half of a rod is uniformly charged with a positive charge density , whereas the right half is uniformly charged with a charge density of . What is the direction of the electric field at a point on the perpendicular bisector and above the rod as shown? a) to the right b) to the left c)  up d) down e) E is zeo.    

12. Lecture 3-12 Physics 241 –Quiz 1b The upper half of a ring is uniformly charged with a positive charge density , whereas the lower half is uniformly charged with a charge density of . What is the direction of the electric field at a point on the perpendicular axis through the center of the ring and to the left of the ring as shown? a) to the right b) to the left c)  up d) down e) E is zeo.    

13. Lecture 3-13 Physics 241 –Quiz 1C The upper half of a rod is uniformly charged with a positive charge density , whereas the lower half is uniformly charged with a charge density of . What is the direction of the electric field at a point on the perpendicular bisector and to the right of the rod as shown? a) to the right b) to the left c)  up d) down e) E is zeo.    