Worked out example

[YMP/EM-02005] Field due to a Uniformly Charged Ring

The electric field due to a charged ring, at a point, \(P\) on its axis,  is computed using Coulomb's law. We will show that the electric field of uniformly charged ring, radius \(R\), at a  point on the axis of the ring,  is given by

\begin{equation}  \vec E = \frac{qz}{4\pi\epsilon_0(z^2+r_0^2)^{3/2}} \, \hat k. \end{equation} where \(q\) is the total charge and \(z\) is the distance if field point from the center of the ring.

[YMP/EM-02008] Electric Field Due to a Dipole

A dipole is a system of two equal and opposite charges separated by a distance. Its electric field is computed and the field at large distances depends only on the dipole moment, defined as the product of the charge and separation between the charges.

While dipole is a system of two charges, the concept of dipole moment is defined and is useful for any system of charges  with total zero charge.

[YMP/EM-04001] Grounded Conducting Sphere and a Point Charge

Two point charges \(Q\) and \(Q^\prime\) are located at positions given by \(\vec{a}, \vec{b},  (a\ne b) \). Find the conditions on \(Q, Q^\prime, a, b \)  so that the potential on the surface of a sphere of radius \(R\) with center at the origin may be zero.

Note the result of this problem is used in solution for electric potential of a grounded conducting sphere in presence of a point charge by the method of images.