Assignment 1
1. Show that .(tV)=( t).V+t( .V), where ‘t’ is a scalar function and V is a vector function.
2. Show that ×(tV)=t( ×V)-V×( t), where ‘t’ is a scalar function and V is a vector.
3. Suppose a region in space is bounded by the paraboloid surface z=x2+y2 and the plane z=1.
Evaluate the flux of a vector
2
ˆ ˆ ˆ
i+xj+zF y k
through this region.
4. Coulombs’ law :
(a) If 13 equal charges are placed at the corners of a 13 sided polygon. What would be the force
on a test charge placed at the center?
(b) If one of the charges are removed what is the force on the test charge.
5. Find the electric field at a distance “z” above the center of a circular loop of radius “r” which
carries a uniform line charge density “ ”.
6. Find the electric field at a distance “z” above the center of a flat disc of radius “R” which carries
a uniform charge density .