Question

The energy required to charge a parallel plate condenser of plate separation d and plate area of cross-section A such that the uniform electric field between the plates is E, is

$1 half straight epsilon subscript straight o straight E squared divided by Ad$
$straight epsilon subscript straight o straight E squared divided by Ad$
$straight epsilon subscript straight o straight E squared Ad$
$1 half straight epsilon subscript straight o straight E squared divided by Ad$

Solution

straight epsilon subscript straight o straight E squared Ad

Energy given be the cell
E =CV²
Here, C = capacitance of condenser = $Aε subscript straight o over straight d$

V = potential difference across the plate = Ed
therefore,

straight E equals space open parentheses Aε subscript straight o over straight d close parentheses space left parenthesis Ed right parenthesis squared equals space Aε subscript straight o straight E squared straight d

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