TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 16

Electromagnetic Field Theory: A Problem Solving Approach Part 16. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Problems 125 Section 35. An infinitely long line charge A is a distance D from the center of a conducting cylinder of radius R that carries a total charge per unit length Ae. What is the force per unit length on the cylinder Hint Where can another image charge be placed with the cylinder remaining an equipotential surface 36. An infinitely long sheet of surface charge of width d and uniform charge density r0 is placed in the yz plane. M W 126 The Electric Field a Find the electric field everywhere in the yz plane. Hint Break the sheet into differential line charge elements dh Oo dy . b An infinitely long conducting cylinder of radius a surrounds the charged sheet that has one side along the axis of the cylinder. Find the image charge and its location due to an incremental line charge element ao dy at distance y . c What is the force per unit length on the cylinder Hint Ị In 1 - cy dy In 1 - cy - 1 37. A line charge A is located at coordinate a b near a right-angled conducting corner. a a Verify that the use of the three image line charges shown satisfy all boundary conditions. b What is the force per unit length on A c What charge per unit length is induced on the surfaces x 0 and y 0 d Now consider the inverse case when three line charges of alternating polarity A are outside a conducting corner. What is the force on the conductor e Repeat a - d with point charges. Section 38. A positive point charge q within a uniform electric field EoL is a distance x from a grounded conducting plane. a At what value of x is the force on the charge equal to zero b If the charge is initially at a position equal to half the value found in a what minimum initial velocity is necessary for the charge to continue on to x 00 Hint Ex dV dx. Problems 127 I 0 ï c If Eo 0 how much work is necessary to move the point charge from x d to x oo 39. A sphere of radius R having a uniformly distributed surface charge Q surrounds a grounded sphere of radius J i. a What is the total charge .

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