A battery does $200 \,J$ of work in charging a capacitor. The energy stored in the capacitor is ......... $J$

  • A

    $200$

  • B

    $100$

  • C

    $50$

  • D

    $400$

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  • [JEE MAIN 2021]

The plates of a parallel plate capacitor have an area of $90 \,cm ^{2}$ each and are separated by $2.5\; mm .$ The capacitor is charged by connecting it to a $400\; V$ supply.

$(a)$ How much electrostatic energy is stored by the capacitor?

$(b)$ View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume $u$. Hence arrive at a relation between $u$ and the magnitude of electric field $E$ between the plates.

How does a capacitor store energy ? And obtain the formula for the energy stored in the capacitor ?