The radius of a metallic sphere if its capacitance is $1/9\,F$, is

  • A

    ${10^6}\,m$

  • B

    ${10^7}\,m$

  • C

    ${10^9}\,m$

  • D

    ${10^8}\,m$

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Assertion : The total charge stored in a capacitor is zero.

Reason : The field just outside the capacitor is $\frac{\sigma }{{{\varepsilon _0}}}$. ( $\sigma $ is the charge density).

  • [AIIMS 2009]

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Answer the following:

$(a)$ The top of the atmosphere is at about $400\; kV$ with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about $100\; Vm ^{-1} .$ Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)

$(b)$ A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area $1\; m ^{2} .$ Will he get an electric shock if he touches the metal sheet next morning?

$(c)$ The discharging current in the atmosphere due to the small conductivity of air is known to be $1800 \;A$ on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged?

$(d)$ What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning? (The earth has an electric field of about $100\; Vm ^{-1}$ at its surface in the downward direction, corresponding to a surface charge density $=-10^{-9} \;C \,m ^{-2} .$ Due to the slight conductivity of the atmosphere up to about $50\; km$ (beyond which it is good conductor), about $+1800 \;C$ is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually all over the globe pump an equal amount of negative charge on the earth.)