0195136047.pdf

12.1 BASIC PRINCIPLES OF ELECTROMECHANICAL ENERGY CONVERSION 511

dWm=

1

2

(

B^2

μ 0

)

Adg

The definition of work gives us

dW=Fdg

whereFis the pulling forceper poleon the bar. While a magnetic pull is exerted upon the bar,

an energydWequal to the magnetic energydWmstored in the magnetic field is expended. Thus,

dWm=dW

or

1

2

(

B^2

μ 0

)

Adg=Fdg

which yields the pulling force per pole on the bar as

F=

1

2

(

B^2

μ 0

)

A

The total pulling on the bar is then given by

Ftotal= 2 F=

(

B^2

μ 0

)

A

F

Bar

N turns

I

g

Core or yoke of uniform

cross-sectional area A

g

Figure E12.1.1Simple magnetic circuit for weight

lifting.

EXAMPLE 12.1.2

Consider the arrangement shown in Figure E12.1.2. A conductor bar of lengthlis free to move
along a pair of conducting rails. The bar is driven by an external force at a constant velocity of
Um/s. A constant uniform magnetic fieldB ̄is present, pointing into the paper of the book page.
Neglect the resistance of the bar and rails, as well as the friction between the bar and the rails.

(a) Determine the expression for the motional voltage across terminals 1 and 2. Is terminal

1 positive with respect to terminal 2?