Two identical non-conducting thin hemispherical shells each of radius R are brought in contact

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1. Electric Charges and Fields

medium

Two identical non-conducting thin hemispherical shells each of radius $R$ are brought in contact to make a complete sphere . If a total charge $Q$ is uniformly distributed on them, how much minimum force $F$ will be required to hold them together

$F = \frac{{{Q^2}}}{{16\pi {\varepsilon _0}{R^2}}}$

$F = \frac{{{Q^2}}}{{32\pi {\varepsilon _0}{R^2}}}$

$F = \frac{{{Q^2}}}{{64\pi {\varepsilon _0}{R^2}}}$

$\frac{{{Q^2}}}{{32\pi {\varepsilon _0}{R^2}}} >F> \frac{{{Q^2}}}{{64\pi {\varepsilon _0}{R^2}}}$

Solution

$\mathrm{F}=$ (Electric pressure) $\times$ (Projected area)

$=\frac{\sigma^{2}}{2 \varepsilon_{0}}\left(\pi r^{2}\right)=\left(\frac{Q}{4 \pi R^{2}}\right)^{2}\left(\frac{1}{2 \varepsilon_{0}}\right) \pi R^{2}$

$\left[ {\frac{{{{\rm{Q}}^2}}}{{32\pi {\varepsilon _0}{{\rm{R}}^2}}}} \right]$

Standard 12

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(KVPY-2017)

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hard

(JEE MAIN-2024)

Two identical non-conducting thin hemispherical shells each of radius $R$ are brought in contact to make a complete sphere . If a total charge $Q$ is uniformly distributed on them, how much minimum force $F$ will be required to hold them together

Solution

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