0195136047.pdf

512 ELECTROMECHANICS

(b) If an electric load resistanceRis connected across the terminals, what are the current and

power dissipated in the load resistance? Show the direction of current on the figure.

(c) Find the magnetic-field force exerted on the moving bar, and the mechanical power

required to move the bar. How is the principle of energy conservation satisfied?

(d) Since the moving bar is not accelerating, the net force on the bar must be equal to zero.

How can you justify this?

B U

(a)

2

1

Conducting

rail

Conducting

rail

Conducting bar

R

dl

l

Figure E12.1.2

B U

I

I

I

(b)

2

1

dl

l

Solution

(a)U, B,andlbeing perpendicular to each other, as per the right-hand rule, the motional

voltage ise=BlU. 1 is positive with respect to 2, since the resulting current (when the

switch is closed) produces a flux opposing the originalB, thereby satisfying Lenz’s law.

(b)I=BlU/R;P=I^2 R=(BlU )^2 /R.

(c) The magnitude of the induced magnetic-field force exerted on the moving bar isBlI, and

it opposes the direction of motion. The mechanical force is equal and opposite to the

induced field force. Hence the mechanical power required to move the bar is

(BlI )U=Bl

BlU

R

U=

(BlU )^2

R

which is the same as the electric power dissipated in the resistor. Energy (from the

mechanical source) that is put in to move the conductor bar is expended (or trans-

ferred) as heat in the resistor, thereby satisfying the principle of energy conserva-

tion.

(d) In order to move the conductor bar at a constant velocity, it is necessary to impress a

mechanical force equal and opposite to the induced field force. Hence the net force on

the bar is equal to zero.