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Two spheres of same metal have radii $a$ and $b$. They have been connected to a conducting wire. Find the ratio of the electric field intensity upon them.
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Verified Answer
The correct answer is:
$b^2 / a^2$.
Since both the metal spheres are connected to the same conducting wire, both of them will be having same charge on them. Let the charge on each of them be $q$.
Then, the electric field intensities are given by,
$$
\begin{aligned}
& E_a=\frac{k q}{a^2}, \quad E_b=\frac{k q}{b^2} \\
& \therefore \frac{E_a}{E_b}=\frac{b^2}{a^2}
\end{aligned}
$$
Then, the electric field intensities are given by,
$$
\begin{aligned}
& E_a=\frac{k q}{a^2}, \quad E_b=\frac{k q}{b^2} \\
& \therefore \frac{E_a}{E_b}=\frac{b^2}{a^2}
\end{aligned}
$$
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