0195136047.pdf

542 ELECTROMECHANICS

Data gathering with various sensors and data reduction have become much easier, automatic,

and quite sophisticated due to the advent of the computer, since the computer can monitor many

inputs, process and record data, furnish displays, and produce control outputs.

Physical

phenomenon

or stimulus

Output

display

Digital

computer

with interface

Analog-to-

digital

conversion

transducerSensor or conditioningSignal Sampling

Figure 12.7.1Block diagram of measurement system using a sensor.

Problems

12.1.1(a) Show by applying Ampere’s circuital law

that the magnetic field associated with a long

straight, current-carrying wire is given by

Bφ=μ 0 I/( 2 πr), where the subscriptφde-

notes theφ-component in the circular cylin-

drical coordinate system,μ 0 is the free-space

permeability,Iis the current carried by the

wire, andris the radius from the current-

carrying wire. What is the net force on the

wire due to the interaction of theB-field

(produced by the currentI) and the currentI?

(b) A magnetic force exists between two adja-

cent, parallel, current-carrying wires. LetI 1

andI 2 be the currents carried by the wires

andrthe separation between them. Use the

result of part (a) to find the force between the

wires. Discuss the nature of the force when

the wires carry currents in the same direction,

and in opposite directions.

*12.1.2A rectangular loop is placed in the field of an in-
finitely long straight conductor carrying a current
ofIamperes, as shown in Figure P12.1.2. Find

an expression for the total flux linking the loop,

assuming a medium of permeabilityμ.

12.1.3Consider a conducting loop of lengthland width

w, as shown in Figure P12.1.3, rotated about its

axis (shown by the broken line) at a speed ofωm

rad/s under the influence of a magnetic fieldB.

(a) Obtain an expression for the induced emf,

assuming the angleθmis zero att=0 and

θm=ωmt.

(b) If a resistorRis connected across terminals

a–a′, explain what happens and how the prin-

ciple of energy conservation is satisfied.

12.1.4A coil is formed by connecting 15 conducting

loops, or turns, in series. Each loop has length

l= 2 .5 m and widthw=10 cm. The 15-turn

coil is rotated at a constant speed of 30 r/s (or

1800 r/min) in a magnetic field of densityB= 2

T. The configuration of Figure P12.1.3 applies.

(a) Find the induced emf across the coil.

(b) Determine the average power delivered to

the resistorR= 500 , which is connected

between the terminals of the coil.

× × × × × × ×

r 1

r 2

r

B

l

I × × × × × × ×

dr

× × × × × × ×

Figure P12.1.2