Electric Field - Electric Field Due to a System of Charges

The Electric field at a point is ______.

1. always continuous.
2. continuous if there is no charge at that point.
3. discontinuous only if there is a negative charge at that point.
4. discontinuous if there is a charge at that point.

Assume that each atom in a copper wire contributes one free electron. Estimate the number of free electrons in a copper wire of mass 6.4 g (take the atomic weight of copper to be 64 g mol⁻¹). 

Two identical blocks are kept on a frictionless horizontal table connected by a spring of stiffness k and of original length l₀. A total charge Q is distributed on the block such that maximum elongation of spring at equilibrium is equal to x. Value of Q is ______.

Show that if we connect the smaller and the outer sphere by a wire, the charge q on the former will always flow to the latter, independent of how large the charge Q is.

An infinite line charge produces a field of 9 × 10⁴ N/C at a distance of 2 cm. Calculate the linear charge density.