1) Answer the following questions.
a. Using Gauss law, derive an expression for the electric field intensity at any point outside a uniformly charged thin spherical shell of radius R and charge density q/A C/m2.
b. Draw the field lines when the charge density of the sphere
i. Positive,
ii. Negative.
c. A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of 100 µC/m2.
Calculate the (i) charge on the sphere (ii) total electric flux passing through the sphere.
2) Using Gauss’s law, derive an expression for the electric field intensity at any point near a uniformly charged thin wire of linear charge density λ C/m.
3) Using Gauss’ law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point
i) Outside and ii) Inside the shell.
Plot a graph showing variation of electric field as a function of r >R and r < R.(r being the distance from the center of the shell.
4) Define electric flux. Write its S.I. units. Using Gauss’s law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it. How is the field directed if i) The sheet is positively charged, ii) Negatively charged?
5) Deduce the expression for the torque acting on a dipole of dipole moment p in the presence of a uniform electric field E.
6) Two point charges +q and – 2q are placed at the vertices B and C of an equilateral triangle ABC of side a as shown in the figure. Obtain the expression for
i. The magnitude and
ii. The direction of the resultant electric field at the vertex A due to these two charges.
