A uniformly charged thin spherical shell of radius R carries uniform surface charge density of - per unit area- It is made of two hemispherical shells- held together by pressing them with force F- F is proportional to -1-0-2 R-21-0-2 R1-0-2- R1-0-2- R-2

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Variation of G Due to Height and Depth

A uniformly c...

Question

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 $F$ . $F$ is proportional to :

\frac{1}{ϵ_{0}} σ^{2} R^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{1}{ϵ_{0}} σ^{2} R

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{ϵ_{0}} \frac{σ^{2}}{R}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{ϵ_{0}} \frac{σ^{2}}{R^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{1}{ϵ_{0}} σ^{2} R^{2}$
As all the four options have same quantites (i.e $σ, R$ and $ϵ_{0}$ ), all we need to do is to just check which option has same dimension as that of force.
We know that $σ \times$ Area = $Q$
$⟹ σ \times R^{2} = Q$
Also, $F = \frac{Q^{2}}{4 π ϵ_{0}}$
$⟹ F = \frac{σ R^{2}}{ϵ_{0}}$ (dimensionally)

Suggest Corrections

Similar questions

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

A thin spherical insulating shell of radius $R$ carries a uniformly distributed charge such that the potential at its surface is $V_{o}$ . A hole with a small area α4πR² (α << 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

Join BYJU'S Learning Program

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. F is proportional to :

The correct option is A 1ϵ0σ2R2As all the four options have same quantites (i.e σ,R and ϵ0), all we need to do is to just check which option has same dimension as that of force. We know that σ×Area = Q ⟹σ×R2=Q Also, F=Q24πϵ0 ⟹F=σR2ϵ0 (dimensionally)

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 $F$ . $F$ is proportional to :