91Ó°ÊÓ

Under what conditions will the electric field intensity be both solenoidal and irrotational?

Write the integral form of the fundamental postulates of clectrostatics in free space. and state their meaning in words.

Calculate the electric force between the electron and nucleus of a hydrogen atom, assuming they are separated by a distance \(5.28 \times 10^{-11}(\mathrm{~m})\).

Two point charges, \(Q_{1}\) and \(Q_{2}\), are located at \((1,2,0)\) and \((2,0,0)\), respectively. Find the relation between \(Q_{1}\) and \(Q_{2}\), such that the total force on a test charge at the point \(P(-1,1,0)\) will have a) no \(x\)-component, b) no \(y^{\circ}\) component.

When the formula for the electric field intensity of a point charge, Eq. (3-12), was derived, a) why was it necessary to stipulate that \(q\) is in a boundless free space? b) why did we not construct a cubic or a cylindrical surface around \(q\) ?

In what ways does the electric field intensity vary with distance for a) a point charge? b) an electric dipole?

Two very small conducting spheres, each of a mass \(1.0 \times 10^{-4}(\mathrm{~kg})\) are suspended at a common point by very thin nonconducting threads of a length \(0.2(\mathrm{~m})\). A charge \(Q\) is placed on each sphere. The electric force of repulsion separates the spheres, and an equilibrium is reached when the suspending thread makes an angle of \(10^{\circ}\). Assuming a gravitational force of \(9.80(\mathrm{~N} / \mathrm{kg})\) and a negiigible mass for the threads, find \(Q\).

State Coulomb's law.

State Gauss's law. Under what conditions is Gauss's law especially useful in determining the electric field intensity of a charge distribution?

Describe the ways in which the electric field intensity of an infinitely long, straight line - charge of uniform density varies with distance?