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A conducting balloon of the radius a is charged to potential V 0 and held at a large height above the earth ensures that charge distribution on the surface of the balloon remains unaffected by the presence of the earth. It is connected to the earth through a resistance R and a valve in the balloon is opened. The gas inside the balloon escapes from valve and the size of the balloon decreases. The rate of decrease in r

Options

  1. Adr dt = 1 4 πε 0 R
  2. Bdr dt =   – 1 4 πε 0 R
  3. Cdr dt = 1 4 πε 0 aR
  4. Ddr dt = - r 4 πε 0 aR

Correct answer

B. dr dt =   – 1 4 πε 0 R

Step-by-step solution

For a sphere V 0 = q 4 πε 0 r , where r is the radius ∴ q = V 0 4 πε 0 r – dq dt = V 0 R – V 0 4 πε 0 dr dt = V 0 R dr dt =   – 1 4 πε 0 R ​​​​

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