AB and CD are two large non parallel metallic plates to a battery as shown. If $σ_{A}$ and $σ_{B}$ be charge densities at points A and B respectively then :

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$σ_{A} \geq σ_{B}$

$σ_{A} > σ_{B}$

$σ_{A} < σ_{B}$

$σ_{A} \leq σ_{B}$

answer is B.

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Detailed Solution

The potential in each of the plate remains same
i.e, $V_{AC} = V_{BD} \Rightarrow E_{AC} \times l_{1} = E_{BD} \times l_{2}$
$\Rightarrow E_{AC} < E_{BD} (as l_{1} > l_{2})$

$\Rightarrow σ_{A} < σ_{B}$

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