A 0.00200-kilogram air inflated balloon is given an excess negative charge, q1 =

Question

A 0.00200-kilogram air inflated balloon is given an excess negative charge, q1 = -3.25 × 10-8 C, by rubbing it with a blanket. It is found that a charged rod can be held above the balloon at a distance of d = 0.0520 m to make the balloon float. In order for this to occur, what polarity of charge must the rod possess? How much charge, q2, does the rod have? Assume the balloon and rod to be point charges. The Coulomb force constant is 1/(4 0) = 8.99 × 109 N·m2/C2 and the acceleration due to gravity g = 9.81 m/s2.

Explanation / Answer

m = mass of ballon = 0.002 kg

q1 = charge on balloon = -3.25 x 10-8 C

q2 = charge on rod

d = distance between balloon and rod = 0.052 m

since the rod is above the balloon and electric force by rod is balancing the weight of balloon. so electric force is attaractive in nature. hence the charge on rod must be opposite to that balloon. so Positive

F = mg

k q1 q2 /d2 = mg

(8.999 x 109) (3.25 x 10-8 ) q2 /(0.052)2 = 0.002 x 9.81

q2 = 18.16 x 10-8 C

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