Multipole Expansion of a Potential

Q. An insulating rod running from \(z=-a to z=a\) carries indicated line charges. Determine the leading term in the multipole expansion of the potential is given by $$ \lambda=kcos(\frac{\pi z}{2a})$$ where k is a constant. Solution: Potential due to multipole...

Removed Charge (Kvpy ’10)

\(12\) positive charges of magnitude \(q\) are placed on a circle of radius \(R\) in a manner that they are equally spaced. A charge \(Q\) is placed at the centre. If one of the charges \(q\) is removed, then the force on \(Q\) is (A) zero (B)$$...

Maximum Electric Field of a Ring

A ring of radius \(r\) is located in the \(x-y\) plane is given a total charge \(Q=2\pi R\lambda\). Show that \(E\) is maximum when the distance \(z=r/\sqrt{2}\). Discussion: The elctric field at distance z from the centre of the ring on the axis of the ring with...

Electric Field of a Charged Hemisphere

A total charge \(q\) is spread uniformly over the inner surface of a non-conducting hemispherical cup of inner radius \(a\). Calculate the electric field. Discussion: Consider a circular strip symmetric about \(z-axis\) of radius \(r\) and width \(ad\theta\) The...

Electric Field from Electric Potential

If the electric potential is given by \(\chi=cxy\), calculate the electric field. Discussion: $$ E_x=-\frac{\partial\chi}{\partial x}=-cy$$ $$ E_y=\frac{\partial \chi}{\partial y}=-cx$$ Hence electric field $$...