(a) (i) Use Gauss' law to obtain an expression for the electric field due to an infinitely long thin straight wire with uniform linear charge density…

Use Gauss' law to obtain an expression for the electric field due to an infinitely long thin straight wire with uniform linear charge density $\displaystyle \lambda$.

An infinitely long positively charged straight wire has a linear charge density $\displaystyle \lambda$. An electron is revolving in a circle with a constant speed $\displaystyle v$ such that the wire passes through the centre, and is perpendicular to the plane, of the circle. Find the kinetic energy of the electron in terms of magnitudes of its charge and linear charge density $\displaystyle \lambda$ on the wire.

Draw a graph of kinetic energy as a function of linear charge density $\displaystyle \lambda$.

Consider two identical point charges located at points $\displaystyle ( 0,0 )$ and (a, $\displaystyle 0$).

Is there a point on the line joining them at which the electric field is zero ?

Is there a point on the line joining them at which the electric potential is zero? Justify your answers for each case.

State the significance of negative value of electrostatic potential energy of a system of charges. Three charges are placed at the corners of an equilateral triangle ABC of side $\displaystyle 2.0$ m as shown in figure. Calculate the electric potential energy of the system of three charges.