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[PLEASE SHOW ALL WORK SO I CAN UNDERSTAND/LEARN][THERE ARE MULTIPLE CHOICE ANSWERS FOR THE QUESTIONS SO YOU KNOW IF YOU ARE ON THE RIGHT TRACK. THEREFORE, IF YOU CALCULATE ONE OF THE NUMBERS THAT YOU SEE IN THE M/C ANSWERS THAN YOU ARE CORRECT SO IT WILL HELP GUIDE YOU][THE MULTPLE CHOICE ANSWERS ARE THE SECOND PICTURE, DON’T FORGET TO SHOW ALL WORK AND BE NEAT][:-):-)]

3. A-9.0 nC charge and a +7 nC charge are located on the x-axis at x=-1.0 cm and x respectively. i. (a) 4.0 cm At what position or positions, between -oo to too, on the x-axis is the electric field zero? (There may be more than one answer... circle ALL of them). i. What is the electric potential at this (these) location? (There may be more than o i. What is the electric potential at this (these) location? (There may be more than one ii. At what position or positions, between-oo to too, on the x axis is the electric potential zero? iv. What is the magnitude electric field at this (these) location? (There may be more than one answer.. circle ALL of them). (There may be more than one answer circle ALL of them). answer... circle ALL of them). (b) Two very small metal "point-sized' spheres with masses 4.0 g and 9.0 g are tied together by a 5.0 cm long massless string and are at rest on a frictionless surface. Each is charged to +6.0 HC. i. What is the energy of this system? ii. What is the tension in the string? ii The string is cut. What is the speed of each sphere when they are far apart? (HINT: You wl eed to use Two conservation laws here.. one of them is Energy Conservation, think will need to use TWO conservation laws here... one of them is Energy Conservation, think back to Physics I for the other).

Explanation / Answer

3ai) There will be ony one location where electric field will be zero and that will be to the right of 7nC

Let the x coordinate be x1

Electric field at x1 due to -9nC = kq/r2 = (9*10-9*9*10-9)/(x1+1)2 towards negative x axis

Electric field at x1 due to 7nC = kq/r2 = (9*10-9*7*10-9)/(x1-4)2 towards positive x axis

Therefore, -(9*10-9*9*10-9)/(x1+1)2 + (9*10-9*7*10-9)/(x1-4)2 =0

9/(x1+1)2 = 7/((x1-4)2

(x1+1)2/9 = (x1-4)2/7

7(x12 + 2x1 + 1) = 9(x12-8x1+16)

Or,  7x12 + 14x1 + 7 = 9x12-72x1+144

Or, 2x12 - 86x1 + 137=0

x1 = 41.34 cm , x1 = 1.66 cm

x1 = 1.66 cm is not possible because it has to be greater than 4cm

Therefore, correct answer is 41.3 cm

Correct option is 4th option

ii) Electric potential at the point due to -9nC   

V = (-9*10-9*9*10-9)/(0.413+.01) = -191.5 V

Electric potential at the point due to 7nC   

V = (9*10-9*7*10-9)/(0.413-0.04) = 168.9 V

Net potential at that point = -191.5+168.9 = -22.6V

Third option is correct

iii) The electric potential will be zero to the right of 7nC charge. Let the x coordinate be x2

Electric potential at x2 due to -9nC = (-9*109*9*10-9)/(x2+1)

Electric potential at x2 due to 7nC = (9*109*7*10-9)/(x2-4)

Total potential = (-9*109*9*10-9)/(x2+1) + (9*109*7*10-9)/(x2-4) = 0

9/(x2+1) = 7/(x2-4)

7(x2+1) = 9(x2-4)

x2 = 21.5 cm

First option is correct

iv) Electric field at this point due to 7nC charge = (9*109*7*10-9)/(0.215-.04)2 = 2057.14 N/C (towards right)

Electric field at this point due to -9nC charge = (9*109*9*10-9)/(0.215+.01)2 = 1600 N/C (towards left)

Total electric field intensity = 2057.14-1600 = 457.14 N/C (towards right)

Fourth option is correct

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