2. Arrays of charges Contents: Basic concept: Sum of forces Linear arrays Example Whiteboards 2-D Arrays Example Whiteboards

3. Basic Concept TOC Three equal positive charges A, B, C The force on B is the sum of the forces of repulsion from A and C ABC F CB F AB

4. Basic Concept TOC Three equal positive charges A, B, C The force on B is the sum of the forces of repulsion from A and C ABC F CB F AB F AB + F CB It’s Vector Time Kiddies!!

5. Linear arrays of charge (Let’s start simple) TOC Find the force on charge B: 1.Calculate the forces 2.Figure out direction 3.Add forces (Vectors) ABC +45  C -15  C +12  C 67 cm 143 cm

6. Linear arrays of charge (Let’s start simple) TOC Find the force on charge B: 1.Calculate the forces 2.Figure out direction 3.Add forces ABC +45  C -15  C +12  C 67 cm 143 cm F CB = kq C q B = -.791 N (to the left, attract) r 2 F AB = kq A q B = 1.101N to the right (repel) r 2

7. Linear arrays of charge (Let’s start simple) TOC ABC +45  C -15  C +12  C 67 cm 143 cm F CB = kq C q B = -.791 N (to the left, attract) r 2 F AB = kq A q B = 1.101N to the right (repel) r 2 +1.101 N-.791 N Finally, +1.101 -.791 = +.31N (To the right)

8. Whiteboards: Linear Charge Arrays 11 | 2 | 323 TOC

9. 41 N left W What is the force on C? Which direction? ABC +120  C -15  C -180  C 70 cm 170 cm F AC = kq A q C = 33.02 (to the left, attract) r 2 F BC = kq B q C = 8.40 N to the left (repel) r 2 = 33.02 left + 8.40 left = 41.42 = 41 N left

10. 4.4 N right W What is the force on A? Which direction? ABC +11  C -140  C +520  C 110 cm 160 cm F CA = kq C q A = 11.44 (to the right, attract) r 2 F BA = kq B q A = 7.05 N to the left (repel) r 2 = 11.44 - 7.05 (left) = 4.39 = 4.4 N right

11. 17.4 N right W What is the force on C? Which direction? ABC +213  C -14  C +213  C 40 cm 130 cm F AC and F BC cancel out F DC = kq D q C = 17.4 N (to the right, repel) r 2 D 90 cm -112  C