Q. Two insulated metal spheres of adii 10 cm and 15 cm charged to a potential of 150V and 100 V respectively are connected by means of a metallic wire. What is the charge on the first sphere?
A) 2 esu
B) 4 esu
C) 6 esu
D) 8 esu
Explanation
(b) Here, $r_{1} = 10\ cm,\ r_{2} = 15\ cm,$
$V_{1} = 150\ V,\ V_{2} = 100\ V\ $
Common potential
$V = \frac{C_{1}V_{1} + C_{2}V_{2}}{C_{1} + C_{2}} = \frac{4\pi\varepsilon_{0}(r_{1}V_{1} + r_{2}V_{2})}{4\pi\varepsilon_{0}(r_{1} + r_{2})}$
= 120 V
$q_{1} = C_{1}\ V = 4\pi\varepsilon_{0}r_{1}V = \frac{10^{- 1}}{9 \times 10^{9}} \times 120C$
$= \frac{12}{9 \times 10^{9}} \times 3 \times 10^{9}\ esu = 4\ $esu
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.