A charge of 1 mu C each is placed on five cor | vedclass

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(D) In a regular hexagon,the distance from each corner to the centre is equal to the side length of the hexagon,$r = 1 \ m$.Let the corners be $A, B,

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$10^{-6} k$

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(D) In a regular hexagon,the distance from each corner to the centre is equal to the side length of the hexagon,$r = 1 \ m$.Let the corners be $A, B, C, D, E, F$ and let the charge be missing at corner $F$.The electric field due to a charge $q$ at a corner is $E = \frac{kq}{r^2}$ directed away from the charge.The electric field due to the charge at $A$ $(E_A)$ and the charge at $D$ $(E_D)$ are equal in magnitude and opposite in direction,so they cancel each other out.Similarly,the electric field due to the charge at $B$ $(E_B)$ and the charge at $E$ $(E_E)$ are equal in magnitude and opposite in direction,so they cancel each other out.The net electric field at the centre is due to the charge at corner $C$ only.$E_{net} = E_C = \frac{kq}{r^2}$Given $q = 1 \mu C = 10^{-6} \ C$ and $r = 1 \ m$:$E_{net} = \frac{k 	imes 10^{-6}}{(1)^2} = 10^{-6} k \ N/C$.

$A$ charge of $1 \mu C$ each is placed on five corners of a regular hexagon of side $1 \ m$. The electric field at its centre is . . . . . . $N$/$C$.

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