MHT CET202619 April 2026Evening ShiftPhysicsElectrostaticsActual
An uniformly charged thin spherical shell of radius 'R' has uniform surface charge density ' '. It is made of two hemispherical identical shells held together by pressing them with force 'F' as shown. F is proportional to [ ₀ = permittivity of free space]
Options
- A1 ₀ , ^2 R^2
- B1 ₀ , ^2 R
- C1 ₀ , ^2 R^2
- D1 ₀ , ^2 R
Correct answer
C. 1 ₀ , ^2 R^2
Step-by-step solution
The electrostatic pressure P on the surface of a uniformly charged thin spherical shell is given by: P = ^2 2 ₀ Consider a small area element dA on the surface of one of the hemispheres. The outward electrostatic force on this element is: dF = P dA = ^2 2 ₀ dA By symmetry, the net force on the hemisphere will be directed along the axis perpendicular to its circular base. The component of the force along this axis is: dF_ = dF = P dA where is the angle between the radially outward normal and the axis of symmetry. In