# 22.8 Torque on a current loop: motors and meters  (Page 2/4)

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The torque found in the preceding example is the maximum. As the coil rotates, the torque decreases to zero at $\theta =0$ . The torque then reverses its direction once the coil rotates past $\theta =0$ . (See [link] (d).) This means that, unless we do something, the coil will oscillate back and forth about equilibrium at $\theta =0$ . To get the coil to continue rotating in the same direction, we can reverse the current as it passes through $\theta =0$ with automatic switches called brushes . (See [link] .)

Meters , such as those in analog fuel gauges on a car, are another common application of magnetic torque on a current-carrying loop. [link] shows that a meter is very similar in construction to a motor. The meter in the figure has its magnets shaped to limit the effect of $\theta$ by making $B$ perpendicular to the loop over a large angular range. Thus the torque is proportional to $I$ and not $\theta$ . A linear spring exerts a counter-torque that balances the current-produced torque. This makes the needle deflection proportional to $I$ . If an exact proportionality cannot be achieved, the gauge reading can be calibrated. To produce a galvanometer for use in analog voltmeters and ammeters that have a low resistance and respond to small currents, we use a large loop area $A$ , high magnetic field $B$ , and low-resistance coils.

## Section summary

• The torque $\tau$ on a current-carrying loop of any shape in a uniform magnetic field. is
$\tau =\text{NIAB}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta ,$
where $N$ is the number of turns, $I$ is the current, $A$ is the area of the loop, $B$ is the magnetic field strength, and $\theta$ is the angle between the perpendicular to the loop and the magnetic field.

## Conceptual questions

Draw a diagram and use RHR-1 to show that the forces on the top and bottom segments of the motor’s current loop in [link] are vertical and produce no torque about the axis of rotation.

## Problems&Exercises

(a) By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength? (b) How many percent would the current need to be increased to return the torque to original values?

(a) $\text{τ}$ decreases by 5.00% if B decreases by 5.00%

(b) 5.26% increase

(a) What is the maximum torque on a 150-turn square loop of wire 18.0 cm on a side that carries a 50.0-A current in a 1.60-T field? (b) What is the torque when $\theta$ is $\text{10}\text{.}9º?$

Find the current through a loop needed to create a maximum torque of $9\text{.}\text{00 N}\cdot \text{m.}$ The loop has 50 square turns that are 15.0 cm on a side and is in a uniform 0.800-T magnetic field.

10.0 A

Calculate the magnetic field strength needed on a 200-turn square loop 20.0 cm on a side to create a maximum torque of $\text{300 N}\cdot \text{m}$ if the loop is carrying 25.0 A.

Since the equation for torque on a current-carrying loop is $\tau =\text{NIAB}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta$ , the units of $N\cdot m$ must equal units of $A\cdot {m}^{2}\phantom{\rule{0.25em}{0ex}}T$ . Verify this.

$A\cdot {m}^{2}\cdot T=A\cdot {m}^{2}\left(\frac{N}{A\cdot m}\right)=N\cdot m$ .

(a) At what angle $\theta$ is the torque on a current loop 90.0% of maximum? (b) 50.0% of maximum? (c) 10.0% of maximum?

A proton has a magnetic field due to its spin on its axis. The field is similar to that created by a circular current loop $0\text{.}\text{650}×{\text{10}}^{-\text{15}}\phantom{\rule{0.25em}{0ex}}m$ in radius with a current of $1\text{.}\text{05}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}A$ (no kidding). Find the maximum torque on a proton in a 2.50-T field. (This is a significant torque on a small particle.)

$3\text{.}\text{48}×{\text{10}}^{-\text{26}}\phantom{\rule{0.25em}{0ex}}N\cdot m$

(a) A 200-turn circular loop of radius 50.0 cm is vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. The Earth’s field here is due north, parallel to the ground, with a strength of $3\text{.}\text{00}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}T$ . What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?

Repeat [link] , but with the loop lying flat on the ground with its current circulating counterclockwise (when viewed from above) in a location where the Earth’s field is north, but at an angle $\text{45}\text{.}0º$ below the horizontal and with a strength of $\text{6.}\text{00}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}T$ .

(a) $\text{0.666 N}\cdot m$ west

(b) This is not a very significant torque, so practical use would be limited. Also, the current would need to be alternated to make the loop rotate (otherwise it would oscillate).

It is more difficult to obtain a high-resolution ultrasound image in the abdominal region of someone who is overweight than for someone who has a slight build. Explain why this statement is accurate.
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it is the force which always opposes the motion of the body
ZAMAN
what is a wave
wave means. A field of study
aondohemba
what are Atoms
aondohemba
is the movement back and front or up and down
sani
how ?
aondohemba
wave is a disturbance that transfers energy through matter or space with little or no associated mass.
lots
A wave is a motion of particles in disturbed medium that carry energy from one midium to another
conist
an atom is the smallest unit( particle) of an element that bares it's chemical properties
conist
what is electromagnetic induction?
conist
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mahmud
How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
How do you convert 0.0045kgcmÂ³ to the si unit?
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Thapelo
Alright Thank you
Falana
Which one is the Bose-Einstein
James
can you explain what plasma and the I her one you mentioned
Olatunde
u can say sun or stars are just the state of plasma
Mohit
but the are more than seven
Issa
list it out I wanna know
Cristal
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fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Xenda
Isn`t fire the plasma state of matter?
Walter
all this while I taught it was plasma
Victor
How can you define time?
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
Tanaya
unpredictable? but I can say after one o'clock its going to be two o'clock predictably!
Victor
how can we define vector
mahmud
I would define it as having a magnitude (size)with a direction. An example I can think of is a car traveling at 50m/s (magnitude) going North (direction)
Hanzo
as for me guys u would say time is quantity that measures how long it takes for a specific condition to happen e.g how long it takes for the day to end or how it takes for the travelling car to cover a km.
conist
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flint
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V=u+at V²=u²-2as
flint
S=ut+½at
flint
they are eqns of linear motion
King
S=Vt
Thapelo
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
King
hi
hello
King
Explain dopplers effect
Not yet learnt
Bob
Explain motion with types
Bob
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Scalar quantity Because acceleration has only magnitude
Bob
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
bhat
its a scalar quantity
Paul
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
Josh
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
fitzgerald
respect to prevailing force
fitzgerald
What is the difference between impulse and momentum?
Manyo
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
fitzgerald
Or I = m(v-u)
fitzgerald
the tendency of a body to maintain it's inertia motion is called momentum( I believe you know what inertia means) so for a body to be in momentum it will be really hard to stop such body or object..... this is where impulse comes in.. the force applied to stop the momentum of such body is impulse..
Pelumi
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K.e=mv² P.e=mgh
Malia
K is actually 1/2 mv^2
Josh
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
John
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
Melody
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Ogor
its a longitudnal wave which is associted wth compresion nad rearfractions
bhat