# Indian Institute of Technology Madras (IIT-M) 2008 A.M.I.E Electrical Engineering Electromagnetic Fields Quiz1 - Question Paper

First Test (25 Marks) Feb 18, 2008

Dept. of Electrical Engineering, IIT Madras

EC301 - Electromagnetic Fields

. Derive your outcomes.

. Draw diagrams wherever it makes sense.

. If you cannot evaluate a few integral and get closed form answers, that does not matter.

But I do want to see clear formulae.

First Test (25 Marks) Feb 18, 2008

Dept. of Electrical Engineering, IIT Madras EC301 - Electromagnetic Fields

[> Derive your results.

[> Draw diagrams wherever it makes sense.

> If you cannot evaluate some integral and get closed form answers, that does not matter. But I do want to see clear formulae.

1. Determine whether the following static fields represent (a) Source free Electric Fields, (b) Source free Magnetic Fields, (c) Electric Fields in the present of charges, (d) Magnetic Fields in the presence of currents, (e) none of the these. If a source is present, find the source.

(a) = 0 cos (kr)

(b) = rcos (kr) sin 0

[3]

[3]

2. A 2-D A container has a width a and a height h. It is filled to a height, h, with oil (with permitivity i). The walls of the container are grounded, but the surface of the oil has some amount of charge, Q trapped on it. The charge can rearrange freely on the surface, but is not allowed to leak to the walls or leave the surface.

x=0

x=a

(a) Show that the oil surface must be at constant voltage. ............. [2]

(b) Solve for the potential in the container, given that the surface is at.............[4]

voltage V

(c) Determine the voltage V, from the total charge on the surface, Q..............[6]

3. A small current loop is present at the origin, with m = m_{0}Z. A second loop of radius z_{0} has its centre at z_{0}Z, and has a current 1_{0} flowing through it, with its magnetisation also pointing in the positive z direction. The value of z_{0} is much larger than the radius of the first loop, so that the approximate field expressions for a current loop apply.

z

y

(a) Determine the magnetic field due to the first coil at points where the current 1_{0} is flowing in the second coil. Note that the vector potential due to a small loop is given by

[3]

/u_{0} m x r 4n r^{3}

A(r) =

(b) Determine the net force on the coil, assuming that it does not deform.

[4]

2

Attachment: |

Earning: Approval pending. |