Question

Two similar conducting spheres having charge+ q and -q are placed at 'd' seperation from each other in air. The radius of each ball is r and the separation between their centre is d (d >> r). Calculate the capacitance of the two ball system ______.

Options

• `4piepsilon_0"r"`

• `2piepsilon_0"r"`

• `4pi log_"e"  (epsilon_0"r")/"d"`

• `4pi log_"e"  ("r")/"d"`

Answer 1

Two similar conducting spheres having charge+ q and -q are placed at 'd' seperation from each other in air. The radius of each ball is r and the separation between their centre is d (d >> r). Calculate the capacitance of the two ball system `underline(2piepsilon_0"r")`.

Explanation:

Step I:

Step II: `"V"_"A" - "V"_"B" = "Kq"/"r" - (- "Kq"/"r") = (2"Kq")/"r"`

Step III: C = `"q"/("V"_"A" - "V"_"B") - "qr"/(2"Kq") = 2piepsilon_0"r"`