16 good questions on electromagnetism

(See attached file for full problem description with proper symbols and diagrams)

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3.1 A long wire carries a current of 2 A along the +z axis. Calculate B in free space at (3,4,9).

3.2 Inside a long conductor of radius a, the magnetic field is H = 5 rho;/(2pi a2) a(phi) A/m. (a) Determine the current density J. (b) Determine the total current carried by the conductor.

3.3 A three-conductor transmission line is configured as shown below. Determine the magnitude and the direction of the magnetic field H at P.

3.5 A transmission line is composed of two parallel (infinitely) long conductors spaced 2-m apart in air. (a) If the magnetic field H at the midpoint between the lines has a magnitude of 100 A/m, determine the current in each conductor of the transmission line. (b) If the direction of the current in each conductor were reversed because of incorrect wiring, how would the magnitude and the direction of the magnetic field at the midpoint change?

3.7 A square loop (0.02 m x 0.02 m) has 100 turns and it lies in the x-y plane. It carries a current of 5 mA. If the loop is exposed to a magnetic flux density B = 2 x 10-3 a Wb/m2 , determine: (a) the magnetic force exerted on the loop; (b) the maximum torque experienced by the loop; (c) If the loop is free to rotate, sketch its equilibrium position.

3.8 A transmission line is composed of two parallel (infinitely) long conductors spaced 2-m apart in air. The conductors carry equal and opposite currents of 100 A each. (a) Determine the magnetic field H (magnitude and direction) at the midpoint between the lines. (b) If both conductors were carrying currents in the same direction, how would the magnitude and the direction of the magnetic field at the midpoint change?

3.10 Two circular loops are centered at the origin in the x-y plane in air. The inner loop has a radius a = 5 cm and it carries a counterclockwise current I1 = 2.5 A. The outer loop has a radius b = 8 cm and it carries a current I2. (a) If the magnetic field at the origin is measured to be zero, determine the magnitude and the direction of I2. (b) If the magnitude of the current in each loop were doubled, how would the magnitude and the direction of the magnetic field at the origin change? Explain.

3.11 A toroid has the following parameters: radius R = 0.1 m; coil radius r = 0.01 m; number of turns N = 1,000; core material = air. (a) If the toroid carries a current of 10 mA, determine the stored magnetic energy. (b) What should be the relative permeability of the core, if we want to increase the stored energy by a factor of 1,000?

3.12 Two long straight wires carry currents of 2 A each in the + a¬z direction. The wires cross the x-y plane at (0, 0, 0) and (4, 0, 0). Determine the magnetic field vector H at: (a) (2, 0, 0); (b) (8, 0, 0).

3.14 Two long straight wires carry currents of 12 A each in the + ax direction. The wires cross the y-z plane at (0, 0, -4) and (0, 0, 4). Determine the magnetic field vector H at: (a) (2, 0, 0) and (b) (0, 0, 8).

3.15 The magnetic field H is given as: H = J0 /3 a A/m for  a and H = J0 a/(3  a A/m for  a. (a) Determine the current density J everywhere. (b) Determine the total current I passing through the annular region a b, located in the x-y plane.

4.1 A square loop (0.1 m x 0.1 m) has 3 turns and it lies in the x-y plane. If the loop is exposed to a time-varying magnetic flux density B = 2 sin (120 pi t) Wb/m2 , determine the maximum value of the induced emf.

4.2 A circular metal loop (radius = 0.1 m) has 100 turns and it lies in the x-y plane. If the loop is exposed to a magnetic flux density B = 2 cos (100 pi t) Wb/m2 , determine: (a) the magnitude of the maximum emf induced in the loop; (b) the direction of current flow during 0 < t < 1/100 s.

4.3 A square loop (0.2 m x 0.2 m) lies in the x-y plane. When the loop is exposed to a magnetic flux density B = 5 x 10-3 cos (2 pi t) Wb/m2 , a sinusoidal emf with a peak value of 62.8 mV is induced in the loop. (a) Determine the frequency f. (b) If the loop had 10 turns, how would the induced emf change?

4.4 A rectangular loop (0.3 m x 0.2 m) has 10 turns and it lies in the y-z plane. It carries a counterclockwise current of 1 A. The loop is exposed to a magnetic flux density B = 5 x 10-3 Wb/m2. (a) Determine the magnitude and the direction of the torque experienced by the loop. (b) If the loop is free to rotate, sketch its equilibrium position.

4.5 A rectangular loop (0.3 m x 0.2 m) has 3 turns and it lies in the x-y plane. If the loop is exposed to a magnetic flux density B = 2 sin (1000 pi t) Wb/m2, determine: (a) the maximum value of the induced emf and (b) the direction of current flow at t = 0. Explain.
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