A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of $σ$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to [2010]

Question

Smart Achievers · Accepted Answer

(1)

The electrostatic force per unit area, i.e., electrostatic pressure at a point on the surface of a uniformly charged sphere $σ$

$∴$ The force on a hemispherical shell $F = \frac{σ^{2}}{2 ε_{0}} \times π R^{2}$

or, $F \propto \frac{σ^{2} R^{2}}{ε_{0}}$

Solution

Q.
A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of $σ$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to [2010]

1 $\frac{1}{ε_{0}} σ^{2} R^{2}$

2 $\frac{1}{ε_{0}} σ^{2} R$

3 $\frac{1}{ε_{0}} \frac{σ^{2}}{R}$

4 $\frac{1}{ε_{0}} \frac{σ^{2}}{R^{2}}$

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Solution

Q. A uniformly charged thin spherical shell of radius R carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to [2010]

1 1ε0σ2R2

2 1ε0σ2R

3 1ε0σ2R

4 1ε0σ2R2