ece259s_2006_exam

# ece259s_2006_exam - UNIVERSITY OF TORONTO Faculty of...

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Unformatted text preview: UNIVERSITY OF TORONTO Faculty of Applied Science and Engineering Final Examination, April 2006 Second Year — Engineering Science ECE259 H1 - Electricity and Magnetism Examination Type: A Examiner: S. Dmitrevsky Assistance: 80 = 8.85x10‘12F/m, yo = 47zx10‘7 All questions are of equal value and any ﬁve constitute a complete paper. Write in ink! Page 1 of 3 pages H/m Two inﬁnite, horizontal, parallel 2 x10'6 m thick layers of positive charge are separated by a 4 x 10'6m wide neutral gap. The charge density of the upper layer is +5 C/m3, that of the lower layer is +2.5 C/m3. An inﬁnite, parallel negative surface charge sheet is located 2 x 10'6 m above the upper layer and another one 2 x 10'6 m below the lower layer. The surface charge density of the upper sheet is -3 x 10'5 C/m2 . The total charge of the system is zero and relative permittivity of the medium, both charged and neutral is 11.3. (i) Plot the electric ﬁelds and, (ii) determine the potential of the lower surface charge layer with respect to ' the upper surface charge layer. Two parallel semi-inﬁnite current lines lying in a horizontal plane are 10cm apart and are aligned in the north-south direction. The 5 ampere current in the eastern one ﬂows north, the return current in the western one ﬂows south. North ends of the lines are connected by a horizontal semicircular loop of 10cm diameter. What is the magnitude and direction of the magnetic ﬂux density vector 10cm above the centre of the semicircular loop? A 10'12 tesla peak amplitude uniform magnetic ﬁeld of 3OMHz frequency lies in a vertical 30" east of north plane and points alternately 45°up and down. The ﬁeld is monitored by a 5 turns loop of 25cm2 area lying in a vertical northwest ~ southeast plane. What is the peak EMF induced in the loop? The inner and outer conductors of a coaxial line are metallic pipes of 5mm outer and 10mm inner radii respectively. The inner conductor is coated by 2mm thick layer of relative permittivity 2.5. What is the electric energy stored in a 1m long section of the line if a 10 volt potential is applied between the inner and outer conductors? Page 2 of 3 pages The moment of an electric dipole is 2 ><10‘9 coulomb meters. The dipole is located 1.5m above conducting ground and points 45 ° up in a north-south vertical plane. What is the surface charge density induced in the ground plane 1.5m south of the dipole location (ie. on the axis of the dipole)? p 0059 2 Assistance: V d= 47:8,, r The electric potential V(x) of a charge distribution is given by the expression V(x) = -E° (ac—g xzz ), with E°=105V/m, d = 2x10'6m. V is independent ofx outside the i 2 x10"6 m range. The relative permittivity of the medium is 1 1.3. (i) Plot a rough sketch of electric ﬁeld identifying numerical values at =0 and i2x10‘6m. (ii) Plot the charge density specifying relevant numerical values and provide a brief verbal description of the charge distribution. Page 3 of 3 pages ...
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ece259s_2006_exam - UNIVERSITY OF TORONTO Faculty of...

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