Identify the product B in the following react | vedclass

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(C) $1$. The reaction of $1$-bromo-$4$-chlorobenzene with $1$ equivalent of $Mg$ in dry ether selectively forms the Grignard reagent at the more react

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Chlorobenzene

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(C) $1$. The reaction of $1$-bromo-$4$-chlorobenzene with $1$ equivalent of $Mg$ in dry ether selectively forms the Grignard reagent at the more reactive $C-Br$ bond,yielding $4$-chlorophenylmagnesium bromide as product $(A)$.$2$. The Grignard reagent $(A)$ acts as a strong nucleophile. It reacts with $2$-chloroethanol $(HO-CH_2-CH_2-Cl)$.$3$. The acidic hydrogen of the hydroxyl group $(-OH)$ in $2$-chloroethanol is abstracted by the Grignard reagent,leading to the formation of chlorobenzene and the alkoxide salt of $2$-chloroethanol. However,in the context of typical organic synthesis questions of this type,if the reaction is intended to be a nucleophilic substitution,it would be problematic due to the acidic proton. Given the options,the reaction is likely intended to be an acid-base reaction where the Grignard reagent is protonated by the $-OH$ group,yielding chlorobenzene. $4$. Re-evaluating the options: Option $(C)$ is chlorobenzene. This is the most chemically sound product of the reaction between a Grignard reagent and an alcohol.

Identify the product $B$ in the following reaction sequence:
$1$-bromo-$4$-chlorobenzene $\xrightarrow[\text{Dry ether}]{Mg (1 \text{ equivalent})} (A)$ $\xrightarrow{HO-CH_2-CH_2-Cl} (B)$

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Identify the product $B$ in the following reaction sequence:$1$-bromo-$4$-chlorobenzene $\xrightarrow[\text{Dry ether}]{Mg (1 \text{ equivalent})} (A)$ $\xrightarrow{HO-CH_2-CH_2-Cl} (B)$