A 2.90-gram air inflated balloon is given an excess negative charge, q 1 = -3.50

Question

A 2.90-gram air inflated balloon is given an excess negative charge, q1 = -3.50 × 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 = 7.20 cm 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.

q2 = ______________ C

Explanation / Answer

Since opposites attract, in order for the rod to hold the balloon up against its weight, and the balloon is negatively charged, the rod must be positively charged.

To find the charge, we know that the force of attraction between the charges is F = kqq/d2.   That must balance the weight of the balloon

kq1q2/d2 = mg

q2 = mgd2/kq1

q2 = (2.9 X 10-3)(9.81)(.072)2/(8.99 X 109)(3.5 X 10-8)

q2 = 4.69 X 10-7 C

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