A large plate of uniform charge density is placed as shown, two cylinders of same volume are at distances $r$ & $2 r$ respectively, if energy (electrostatic) stored in them are $U_{A}$ & $U_{B}$ respectively then,

U_{A} : U_{B} = 4 : 1

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U_{A} : U_{B} = 1 : 1

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U_{A} : U_{B} = 1 : 4

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U_{A} : U_{B} = 8 : 1

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Solution

The correct option is B $U_{A} : U_{B} = 1 : 1$
Energy = Energy density $\times$ volume
$= \frac{1}{2} \in_{0} E^{2} \times (V o l u m e)$
$\frac{U_{A}}{U_{B}} = \frac{\frac{1}{2} \in_{0} E_{A}^{2} \times V o l u m e}{\frac{1}{2} \in_{0} E_{B}^{2} \times V o l u m e} = {(\frac{E_{A}}{E_{B}})}^{2} = 1 : 1$
Field is independent of distance in case of charged sheet.

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A large plate of uniform charge density is placed as shown, two cylinders of same volume are at distances r & 2r respectively, if energy (electrostatic) stored in them are UA & UB respectively then,

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A large plate of uniform charge density is placed as shown, two cylinders of same volume are at distances $r$ & $2 r$ respectively, if energy (electrostatic) stored in them are $U_{A}$ & $U_{B}$ respectively then,