Question

The minimum strength of a uniform electric field which can tear a conducting uncharged thin-walled sphere into two parts is known to be E₀.

Determine the minimum electric field strength E₁ required to tear the sphere of twice as large radius if the thickness of its walls is the same as in the former case.

Answer 1

The density of charges induced on the sphere is proportional to the electric field strength: σ ∝ E. The force acting on the hemispheres is proportional to the field strength:

where S is the area of the hemisphere, and R is its radius. As the radius of the sphere changes by a factor of n, and the field strength by a factor of k, the force will change by a factor of k²n². Since the thickness of the sphere walls remains unchanged, the force tearing the sphere per unit length must remain unchanged, i.e. k²n²/n = 1 and k = 1/√n = 1/√2. Consequently, the minimum electric field strength capable of tearing the conducting shell of twice as large radius is