IIT-JEE 2010 · Paper 2 · Physics Q44

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PhysicsSingle correct+5 / -2Question 44 of 57

A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to

A circle (the spherical shell) split by a vertical dashed line into two hemispheres; equal and opposite horizontal forces F push the two halves together from left and right.

\dfrac1{\varepsilon_0}\sigma^2R^2

\dfrac1{\varepsilon_0}\sigma^2R

\dfrac1{\varepsilon_0}\dfrac{\sigma^2}R

\dfrac1{\varepsilon_0}\dfrac{\sigma^2}{R^2}

Answer and worked solution

Official answer: A

Electrostatic pressure on a charged conducting-type shell: $p=\dfrac{\sigma^2}{2\varepsilon_0}$ , outward.

Net force on a hemisphere. Integrating the pressure over the hemisphere gives the pressure times the projected area $\pi R^2$ :
$F=\frac{\sigma^2}{2\varepsilon_0}\pi R^2.$
So $F\propto\dfrac{\sigma^2R^2}{\varepsilon_0}$ .

(A)

Topics:Conductors and charge distribution

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IIT-JEE 2010 · Paper 2, Physics question 44