Question

Two small, identical spheres, one positively charged and another negatively charged are placed 0.5m apart attract each other with a force of 0.108N. If they are brought in contact for some time and again separated by 0.5m, they repelled each other with force of 0.036N. What were the initial charges on the spheres ?

Answer 1

Answer:

1μC and 3μC

Explanation:

F1 = 0.108 N  (Given)

F2 = 0.036 N  (Given)

r = 0.5 m  (Given)

Let the charges on the spheres be q1 and q2

According to the conservation of charge

= q1 + q2 = 2q  ----- 1

F1 = k q1q2/r²  ==---2

F2 = k q2/r²   ------3

= 0.036 = 9×10`9×q2/(0.5)²

= q2 = 0.036×(0.5)²/9×10`9

= q2 = 0.036/(4×9×10`9)

= q = 1×10`-6 C    -----4

From equation 2 and 3  we will get -

F1/F2 = q1q2/q2

= 3 = q1q2/q2

= 3q² = q1q2

= q1q2 = 3q2²

Hence,

(q1 – q2)² = (q1 + q2)² – 4q1q2

= (2q)² – 3q2/ r²

= q²/ r²

By using equation 4 we will get -  

(q1 – q2)  = q/r

= 1×10-6/ 0.5

= 2×10-6    -----5

From equation 1 and 4 we will get -  

q1 + q2 = 4×10-6  ---6.

Adding equation 5 and 6

q1 = 3×10-6

= 3μC

q2 = 1×10-6  (On subtraction)

= 1μC