Download Assignment problems

Assignment problems
Chapter-1
1. In the Cartesian coordinate system; verify the following relations for a scalar
function V and a vector function A
(a)   V   0


(b)   A  0


(c)  (VA)  V  A   V   A
2. An electric field expressed in spherical polar coordinates is given by E 
9
aˆr .
r2
Determine E and E y at a point P (1, 2, 2) .
3. Evaluate

S
sin 
aˆr dS over the surface of a sphere of radius r0 centered at the
r02
origin.
4. Find the divergence of the radial vector field given by f  r   aˆr r n .
5.
A vector function is defined by A  xy 2 aˆ x  yx 2 aˆ y . Find
contour shown in the figure……... Evaluate


verify that  A dl    A ds .
Fig…….
 A dl around
the
    A ds over the shaded area and
Chapter 2
1. A charged ring of radius d carrying a charge of  L C/m lies in the x-y plane with
its centre at the origin and a charge Q C is placed at the point (0, 0, 2d ) .
Determine  L in terms of Q and d so that a test charge placed at (0, 0, 2d ) does
not experience any force.
2. A semicircular ring of radius a lies in the free space and carries a charge density
 L C/m. Find the electric field at the centre of the semicircle.
3. Consider a uniform sphere of charge with charge density o and radius b,
centered at the origin. Find the electric field at a distance r from the origin for
the two cases: r<b and r>b. Sketch the strength of the electric filed as function of
r.
4. A spherical charge distribution is given by
 0 (a 2  r 2 ),
v  
0,

ra
ra
a is the radius of the sphere. Find the following:
(i)
(ii)
The total charge.
E for r  a and r  a .
The value of r where the E becomes maximum.
(iii)
5. With reference to the Fig. ___ determine the potential and field at the point
P (0, 0, h) if the shaded region contains uniform charge density  s /m2.
6. A capacitor consists of two coaxial metallic cylinders of length L , radius of the
inner conductor a and that of outer conductor b . A dielectric material having
dielectric constant  r  3  2 /  , where  is the radius, fills the space between the
conductors. Determine the capacitance of the capacitor.
7. Determine whether the functions given below satisfy Laplace’s equation
1
(i)
V ( x, y , z ) 
(ii)
V (  ,  , z )   z sin    2
x2  y 2  z 2
8. A point charge Q is placed at a distance d from a large grounded
conducting plane. Let us consider a region on the grounded plane bounded
between two concentric circles of radii d and 2d respectively. The
circles are placed vertically below the point charge in such a way that
their centers are exactly below the point charge. If the region under
consideration shows a total charge of 1 C , determine the charge Q .