Download Q No - Air University

Air University
Mid Term Examination
(Spring-2013)
Course: Electricity and Magnetism (EE-211)
Date: 25-03-2013
Instructors: Drs. Muhammad Atif and Rubina Nasir
Max. Marks: 30
Total Time: 2 hrs
Note: Attempt all 5 questions. Use appropriate units for all answers and proper vector notation when required.
Draw clear diagrams for all questions where required.
Q No. 1: The Potential of a field (in Volts) is given by
V(x, y) = 10(2xy - 3x2 – 4y2 - 18x + 28y + 12)
where x and y are the distance in meters.
(a) Where is the maxima of this potential occurs in space?
(2)
(b) What is the maximum of this potential?
(2)
(c) How steep is the slope of this potential (in volts per meter) at a point (1,1)? Also find the
corresponding electric field, at that point?
(2)
Q No. 2: Is the given electric field E conservative
E = (r cos2θ) r - (r cosθ sinθ) θ + (3r) φ.
If not, compute the line integral of this field around the path shown in the Fig. 1. Also check your
answer using Stokes' theorem.
(2+2+2)
Q No. 3: (a) Calculate the electric field due to electric dipole at point R having polar coordinates r and
θ, as shown in Fig. 2.
(4)
(b) A dipole is consisting of an electron and proton, 4x10-10 m apart. Calculate the electric field at a
distance of 2x10-8 m on a line making an angle of 45o with the dipole axis from the centre of the
dipole.
(2)
Q No. 4: Prove that the divergence of the electric field vanishes outside the spherically symmetric
charge distribution but not inside the distribution.
(6)
Q No. 5: (a) For the case of a uniformly charged conducting spherical shell of radius R (Fig. 3), show
that electric potential at some external point varies inversely as distance from its centre whereas the
potential at some internal point is constant, the same as that on its surface.
(4)
(b) For a conservative field, show that electric field (obtained from part (a)) outside the charged sphere
varies inversely as square of distance but is zero inside the sphere.
(2)
R (r,θ)
θ
-Q
O
p
+Q
2d
Figure 1
Figure 2
Figure 3