8/18/2019 2007 Electromagnetics One Midterm

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2007 Electromagnetics one Midterm

1.  Find the algebraic equation for the direction lines for the vector field given in spherical coordinates by

(5cosθ+sinθ)

2.  (a) What is the Biot-Savart law? State its mathematical expression.

(b) Is it exactly valid for computing the magnetic field due to a time-varying current distribution?

3.  (a) What is Gauss' law for the electric field? Describe it both in integral form and in differential form.

(b) Is it valid for the case of time-varying source and field distribution?

4.  In a Cartesian coordinate system, constant current I flows along a straight wire from a point charge Q1(t)

located at the origin to a point charge 2()  located at (0,0,5) 

(a) Find the line integral of magnetic field H along the square closed path having the vertices at

(5,5,0), (5,5,0), (5, 5,0)  and (5,5,0)and traversed in that order. (Express the answer in

terms of current I)

(b) If the current I is time-varying, i.e.,I=I(t),(0