The electric field due to a point charge 2q a | vedclass

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(B) For a point charge $2q$ at distance $r$, the electric field is $E = k \frac{2q}{r^2}$.For a thin spherical shell of charge $q$ and radius $R$, the

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$2E$

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(B) For a point charge $2q$ at distance $r$, the electric field is $E = k \frac{2q}{r^2}$.For a thin spherical shell of charge $q$ and radius $R$, the electric field at a distance $r' = \frac{r}{2}$ from the center is considered. Since $r \gg R$, the condition $r' > R$ is satisfied, meaning the shell acts as a point charge at its center.Thus, $E' = k \frac{q}{(r/2)^2} = k \frac{q}{r^2/4} = 4k \frac{q}{r^2}$.From the first equation, $k \frac{q}{r^2} = \frac{E}{2}$.Substituting this into the expression for $E'$, we get $E' = 4 	imes \frac{E}{2} = 2E$.Therefore, the correct option is $B$.

The electric field due to a point charge $2q$ at a distance $r$ is $E$. Now, if charge $q$ is uniformly distributed over a thin spherical shell of radius $R$, the electric field at a distance $\frac{r}{2}$ $(r \gg R)$ from the center of the thin spherical shell is $E'=$ . . . . . . .

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