A conducting rod with a weight of 2.00 N and a length of 3.00 m can slide with n

Question

A conducting rod with a weight of 2.00 N and a length of 3.00 m can slide with no friction down a pair of vertical conducting rails, as shown in the figure below. The rails are joined at the bottom by a lightbulb of resistance 5.00 ohms. The rails have stops near the bottom to prevent the rod from smashing the bulb. There is a uniform magnetic field of magnitude 6.00 T directed out of the page. When the rod is released from rest, the force of gravity causes the rod to accelerate down the rails, but the rod eventually reaches a terminal velocity (that is, it falls at constant speed).

(a) Choose all the correct statements about this situation. (Select all that apply.)

While the rod is falling, the current is always directed clockwise around the loop.

While the rod is falling, the current is always directed counterclockwise around the loop.

Once the rod reaches its terminal velocity, there is no current.

Once the rod reaches its terminal velocity, the current is constant.

The faster the rod moves, the brighter the lightbulb is.

The lightbulb is brightest at the beginning, and then, gradually, the bulb gets dimmer as the rod gets closer to its terminal velocity.

(b) What is the magnitude of the maximum current in this situation?


(c) What is the magnitude of the maximum induced voltage in this situation?


(d) What is the rod's terminal speed?

Explanation / Answer

(a)

While the rod is falling, the current is always directed counterclockwise around the loop

Once the rod reaches its terminal velocity, the current is constant

The faster the rod moves, the brighter the lightbulb is

(b)

to get the maximum current first we must find the velocity

v = m g R / B2l2

= (200) (5) / (36) (9)

= 3.086 m / s

the current is given by

i = B l v / R

= (6) (3) (3.086) / (5)

= 11.11 A

maximum induced voltage will be

e = B l v

= (6) (3) (3.086)

= 55 V

(d)

terminal speed will be

v = 3.086 m / s

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