Question

Each of two small spheres is charged positively, the total charge being 52.6 µC. Each sphere is repelled from the other with a force of 1.19 N when the spheres are 1.94 m apart. Calculate the charge on each spher

Answer 1

q1= 4.26×10^-6C

q2= 1.0×10^-6C

Step-by-step explanation:

q1+q2= 5.26×10^-6C

F=1.19N

F= kq1q2/r^2 =1.19

q1q2= (1.19)(r^2/k)

q1q2= 1.19×(1.94^2)×8.99×10^9=4.026×10^-10C^2

q2= 5.26×10^-6 -q2 ....eq1

q1q2=4.026×10^-10 .....eq2

Put eq1 into eq2

q1(5.26×10^-6)- q1=4.026×10^-10

5.26×10^-6q1-q1^2-4.026×10^-10

q1^2-(5.26×10^-6)q1 +4.026×10^-10

Using almighty formular to solve the quadratic equation

= 5.26×10^-6 +-sqrt(5.26×10^-6)^2 -4(4.026×10^-10) /2

q1=5.26×10^-6 +-sqrt(1.065x10^-11)/2

q1= (5.26×10^-6 )+-3.26×10^-6/2

q1= (2.26×10^-6) + 3.26×10^-6/2

q1= 4.26×10^-6C

q2= (5.26×10^-6 ) -(3.26×10^-6)/2

q2= 1.0×10^-6C