PART A
1.State stokes theorem.
The line integral of a vector around a closed path is equal to the surface integral of the normal component of its curl over any surface bounded by the path
H.dl = (▼xH)ds
2.Define divergence.
The divergence of a vector F at any point is defined as the limit of its surface integral per unit volume as the volume enclosed by the surface around the point shrinks to zero.
3.State Divergence Theorem.
The integral of the divergence of a vector over a volume v is equal to the surface integral o f the normal component of the vector over the surface bounded by the volume.
4.What is the physical significance of div D ?
▼•D= ρv
The divergence of a vector flux density is electric flux per unit volume leaving a small volume. This is equal to the volume charge density.
5.State the condition for the vector F to be solenoidal.
▼•F =0
6. .State the condition for the vector F to be irrotational.
▼xF =0
7.Describe what are the sources of electric field and magnetic field?
Stationary charges produce electric field that are constant in time, hence the term electrostatics. Moving charges produce magnetic fields hence the term magnetostatics.
PART-B
1. Derive electric field intensity at the given point due to line charge of infinite length.
2. State and prove divergence theorem for electric field.
3. Apply Gauss’s law to an unsymmetrical field.
4. Apply Gauss’s law to an
a) infinite line charge
b) infinite sheet of charge.
5. Define dipole. Derive the electric field intensity, E and the potential due to a dipole.
6. Obtain the expression for energy density in an electrostatic field.
7. Point charge 1mC and -2mC are located at (3,2,-1) and (-1,-1,4) respectively. Calculate the electric force on a 10nC charge located at (0,4,1) and electric field intensity at that point.
8. A circular ring of radius ‘a’ carries a uniform charge L C/m and is placed on the XY plane with the axis same as z axis. Find the electric field intensity.
9. If G(r)= 10e-2z (r ar+az), determine the flux of G(r ) out of entire surface of the cylinder r=1
10. Two point charges are located at points P1(-1, 0,0) and P2(1,0,0). The charge at P1 is 1C and the charge at P2 is -2 C. find the location on the X axis where a positive test charge will not experience any force. Distance are in meters.
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