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The torque found in the preceding example is the maximum. As the coil rotates, the torque decreases to zero at θ = 0 size 12{θ=0} {} . The torque then reverses its direction once the coil rotates past θ = 0 size 12{θ=0} {} . (See [link] (d).) This means that, unless we do something, the coil will oscillate back and forth about equilibrium at θ = 0 size 12{θ=0} {} . To get the coil to continue rotating in the same direction, we can reverse the current as it passes through θ = 0 size 12{θ=0} {} with automatic switches called brushes . (See [link] .)

The diagram shows a current-carrying loop between the north and south poles of a magnet at two different times. The north pole is to the left and the south pole is to the right. The magnetic field runs from the north pole to the right to the south pole. Figure a shows the current running through the loop. It runs up on the left side, and down on the right side. The force on the left side is into the page. The force on the right side is out of the page. The torque is clockwise when viewed from above. Figure b shows the loop when it is oriented perpendicular to the magnet. In both diagrams, the bottom of each side of the loop is connected to a half-cylinder that is next to a rectangular brush that is then connected to the rest of the circuit.
(a) As the angular momentum of the coil carries it through θ = 0 size 12{θ=0} {} , the brushes reverse the current to keep the torque clockwise. (b) The coil will rotate continuously in the clockwise direction, with the current reversing each half revolution to maintain the clockwise torque.

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 θ size 12{θ} {} by making B size 12{B} {} perpendicular to the loop over a large angular range. Thus the torque is proportional to I size 12{I} {} and not θ size 12{θ} {} . A linear spring exerts a counter-torque that balances the current-produced torque. This makes the needle deflection proportional to I size 12{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 size 12{A} {} , high magnetic field B size 12{B} {} , and low-resistance coils.

Diagram of a meter showing a current-carrying loop between two poles of a magnet. The torque on the magnet is clockwise. The top of the loop is connected to a spring and to a pointer that points to a scale as the loop rotates.
Meters are very similar to motors but only rotate through a part of a revolution. The magnetic poles of this meter are shaped to keep the component of B size 12{B} {} perpendicular to the loop constant, so that the torque does not depend on θ size 12{θ} {} and the deflection against the return spring is proportional only to the current I size 12{I} {} .

Section summary

  • The torque τ size 12{τ} {} on a current-carrying loop of any shape in a uniform magnetic field. is
    τ = NIAB sin θ , size 12{τ= ital "NIAB""sin"θ} {}
    where N size 12{N} {} is the number of turns, I size 12{I} {} is the current, A size 12{A} {} is the area of the loop, B size 12{B} {} is the magnetic field strength, and θ size 12{θ} {} 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.

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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) τ size 12{" τ"} {} decreases by 5.00% if B decreases by 5.00%

(b) 5.26% increase

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(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 θ size 12{θ} {} is 10 . 9º? size 12{"10" "." 9°?} {}

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Find the current through a loop needed to create a maximum torque of 9 . 00 N m. size 12{9 "." "00"`N cdot 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

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Calculate the magnetic field strength needed on a 200-turn square loop 20.0 cm on a side to create a maximum torque of 300 N m size 12{3"00"`N cdot m} {} if the loop is carrying 25.0 A.

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Since the equation for torque on a current-carrying loop is τ = NIAB sin θ size 12{τ= ital "NIAB""sin"θ} {} , the units of N m size 12{N cdot m} {} must equal units of A m 2 T size 12{A cdot m rSup { size 8{2} } `T} {} . Verify this.

A m 2 T = A m 2 N A m = N m size 12{A cdot m rSup { size 8{2} } cdot T=A cdot m rSup { size 8{2} } left ( { {N} over {A cdot m} } right )=N cdot m} {} .

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(a) At what angle θ size 12{θ} {} is the torque on a current loop 90.0% of maximum? (b) 50.0% of maximum? (c) 10.0% of maximum?

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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 . 650 × 10 15 m size 12{0 "." "650" times "10" rSup { size 8{ - "15"} } `m} {} in radius with a current of 1 . 05 × 10 4 A size 12{1 "." "05" times "10" rSup { size 8{4} } `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 . 48 × 10 26 N m size 12{3 "." "48" times "10" rSup { size 8{ - "26"} } `N cdot m} {}

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(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 . 00 × 10 5 T size 12{3 "." "00" times "10" rSup { size 8{ - 5} } `T} {} . What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?

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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 45 . size 12{"45" "." 0°} {} below the horizontal and with a strength of 6. 00 × 10 5 T size 12{6 "." "00" times "10" rSup { size 8{ - 5} } `T} {} .

(a) 0.666 N m size 12{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).

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Questions & Answers

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.
Lanii Reply
What is the frictional forc e between two bodies
Kennedy Reply
it is the force which always opposes the motion of the body
ZAMAN
what is a wave
Williams Reply
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
what's boy's law
mahmud
How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
Larissa Reply
How do you convert 0.0045kgcm³ to the si unit?
EDYKING Reply
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
Falana Reply
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
what the meaning of continuum
Akhigbe Reply
What state of matter is fire
Thapelo Reply
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?
Thapelo Reply
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
what is the relativity of physics
Paul Reply
How do you convert 0.0045kgcm³ to the si unit?
flint
What is the formula for motion
Anthony Reply
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
Mehadi
hello
King
Explain dopplers effect
Jennifer Reply
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.
Alabi Reply
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
Calculation of kinetic and potential energy
dion Reply
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
what is sound wave
Nworu Reply
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
Ogor
its a longitudnal wave which is associted wth compresion nad rearfractions
bhat
Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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