1. Coulomb’s Law (Force Between Charges) -- + + + - qeqe qeqe qeqe qpqp qpqp qpqp F F F F F F d The forces are equal and opposite.

2. + + + + + + - - - q1q2 d F F The forces are equal and opposite regardless of the size of the charge of either body.

3. Coulomb’s Law k=9.00x10 9 Nm 2 /C 2

4. How much force exists between a proton and electron that are separated by 1.0 m? F=2.3 x 10 -28 N How much force exists between -2.0μC and +4.0 μC of charge separated by 1.5 mm? F=3.2x10 4 N

5. The Net Force on a Charge q A =+5.0μC q B =+8.0μC q C =-2.0μC What is the resultant force of charge on q C ? d=1.0 mmd=2.5 mm F CA =-9.0x10 4 NF CB =+2.3x10 4 N F C = F CA +F CB = -6.7x10 4 N fixed

6. qAqA qBqB d AB F AC =F AB What magnitude and charge type, qc, is necessary for q A to be in electrostatic equilibrium if q A =2.0μC and q B =7.0 μC? Charge C will be place 3.0 mm from charge A. The distance between charges A and B is 11 mm. -5.2x10 -7 C= -.52 μC +- fixed 3.2x10 12 electrons - d AC qCqC fixed Known: q A, q B, d AC, d AB

7. - qAqA qCqC qBqB L xL-x F CA =F CB A 2.0 μC charge (q A ) at the origin and 4.0 μC (q C ) body are separated by 1.0 m. Where must a third charge be placed between the two charges for qB to be in equilibrium?.41 m from q A (.59 m from q B ) Case 1: Two like bodies of charge fixed A 2.0 μC charge (q A ) at the origin and 4.0 μC (q B ) body are separated by 1.0 m. Where must a third charge, q C be placed for electrostatic equilibrium? What must be the sign of the third charge? - Known: q A, q B, q C, L

8. - - qAqA qCqC qBqB L x F CA =F CB A 2.0 μC charge (q A ) at the origin and 4.0 μC (q C ) body are separated by 1.0 m. Where must a third charge be placed between the two charges for qB to be in equilibrium? 0.64 cm from q B (1.64 cm from q A ) Case 2: Two like unlike charges fixed A 13 μC body of charge (q A ) at the origin and a 2.0 μC (q B ) body are separated by 1.0 cm. Where must a third charge, q C be placed for electrostatic equilibrium? + Known: q A, q B, q C, L

9. Equilibrium of a Charge qAqA qBqB qCqC L+x xL F BA =F BC A 2.0 μC (q B ) body at the origin and 4.0 μC (q C ) body are separated by 1.0 m. Where must a third charge be placed outside of the system for there to be equilibrium? 2.3 m to the left of charge B (3.3 m to the left of charge C). Determination of charge location for system equilibrium.

10. Equilibrium of a Charge qCqC qAqA qBqB L dAdA dBdB F A =F B What magnitude qc is necessary for q B to be in equilibrium if q A =2.0μC and q C =1.60mC? The distance between charges A and B is 1.3 km and the distance between charges B and C is.89 km? 3.4x10 -3 C= 3.4 mC Determination of a charge location to cause equilibrium.

11. Can q A and q C be opposite charges for q B to be in equilibrium between the two charges? - ++ qAqA qCqC