1. Consider a solid circular disc of radius a lying in the xy-plane with its center...

 

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1. Consider a solid circular disc of radius a lying in the xy-plane with its center at the origin and carrying charge of density 47/r C/m². Obtain the expression for the electric field intensity at the point (0,0,z). 2. A circular loop of wire of radius a is situated in the xy-plane with its center at the origin. It carries a current I in the clockwise sense as seen along the positive z-axis (increasing value of o). Obtain the expression for B at a point on z-axis. 3. Find the displacement flux emanating from the following charge distributions: (a) p(x, y, z) = p. (3-x² - y²-2²) for the cubical box bounded by x = ±1, y = ±1, and z = ±1; (b) p(x, y, z) = p. (xyz) for x>0, y>0, z>0 and x² + y² + z² <1; (c) p(r.o.z) = p. exp(-²) for r < 1 and 0 <z<1; (d) p(r.o.0) = p sin² 0/r for r < 1 and 0 <0</2. 4. A coaxial cable consists of an inner conductor of radius 3a and an outer conductor of inner radius 4a and outer radius 5a. Assume the cable to be infinitely long and its axis along z-axis. Current I flows with uniform density in the +z-direction in the inner conductor and returns with uniform density in the -z-direction in the outer conductor. Find H everywhere and plot H, versus r. 1. Consider a solid circular disc of radius a lying in the xy-plane with its center at the origin and carrying charge of density 47/r C/m². Obtain the expression for the electric field intensity at the point (0,0,z). 2. A circular loop of wire of radius a is situated in the xy-plane with its center at the origin. It carries a current I in the clockwise sense as seen along the positive z-axis (increasing value of o). Obtain the expression for B at a point on z-axis. 3. Find the displacement flux emanating from the following charge distributions: (a) p(x, y, z) = p. (3-x² - y²-2²) for the cubical box bounded by x = ±1, y = ±1, and z = ±1; (b) p(x, y, z) = p. (xyz) for x>0, y>0, z>0 and x² + y² + z² <1; (c) p(r.o.z) = p. exp(-²) for r < 1 and 0 <z<1; (d) p(r.o.0) = p sin² 0/r for r < 1 and 0 <0</2. 4. A coaxial cable consists of an inner conductor of radius 3a and an outer conductor of inner radius 4a and outer radius 5a. Assume the cable to be infinitely long and its axis along z-axis. Current I flows with uniform density in the +z-direction in the inner conductor and returns with uniform density in the -z-direction in the outer conductor. Find H everywhere and plot H, versus r.

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