Question

The gecko is sticking upside down to a smooth ceiling. The remarkable adhesion might be due to static electricity. Gecko feet are covered with microscopic hairs. When these hairs rub against a surface, charges separate, with the hair developing a positive charge and negative charge forming below the surface. There is an attractive force between the separated charges. This is an effective means of adhering to a surface, but it comes at a cost: Two planes of charge are like two charged plates of a capacitor, which takes energy to charge. Doubling the amount of charge on each surface increases the attractive force, but also increases the energy required to separate the charge. By what factor will this energy increase?

Answer 1

By a factor of 4

Step-by-step explanation:

Consider a simple capacitor instead of the whole story to simplify the problem.

Work done in separating charges = Energy stored in the capacitor (assuming no energy loss happens)

And we know,

Energy stored in the capacitor (E) = VQ/2

and Q=CV

where V= potential difference

Q = charge stored

C = Capacitance

We get, E =
`(Q^(2) )/(2C)`

and we know Capacitance (C) = εA/d

A = surface area , ε = permitivity, d = distance between two plates

By the above equation C remains constant for gecko for what ever charge as ε depends only on material.

So you get, E ∝
`Q^(2)`

So charge increased by two gives the energy required to rise by factor of 4