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Unformatted text preview: Electromagnetics Tutorial Prof. S. Peik Tutorial 1 : Charges, Electrostatics Problem 1: A thin wire in the xy-plane as shown is charged with a line charge density, that depends on the coordinate x (in meter) by λ ( x ) = λ x 2 1 m (1) y x 1 1 λ (x)-1 1. Find the total charge on the wire 2. Find the E-Field in the origin 3. Find the potential at the origin 4. Sketch the E-field lines and the equal potential lines Problem 2: A capacitor is formed from three identical conducting spheres in a regular triangle as shown. The radius of the spheres is R = R . The spheres are at a distance d = 4 R apart. The medium is vacuum. d d d 1 3 2 1. Sketch an equivalent circuit 2. Find the total capacitance between terminal 1 and 3 as a function of R 3. We set the potential at terminal one to V 1 = V and apply V 13 = 100V between terminal 1 and three. Terminal two is open. The Radius is now R = 1 cm . Find the total charge and the potential on each sphere. 4. Sketch the field pattern and the charge distribution on the spheres for 3. Be precise with the charge locations! Stand: December 4, 2009 1 Electromagnetics Tutorial Prof. S. Peik Tutorial 2 : Capacitance Problem 3: Below shown are three planar dielectric slabs of equal thickness but different dielectric constants. If vector E in air makes an angle of 45 o with respect to the slab surface find the angles of the E-field in the three layers....
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