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(a) What is the maximum torque on a 150 -turn square loop of wire 18.0 $\mathrm{cm}$ on a side that carries a 50.0 -A current in a 1.60 -T field? (b) What is the torque when $\theta$ is $10.9^{\circ}$ ?
Part $(\mathrm{a}) :$ The maximum torque is 360 $\mathrm{N} \cdot \mathrm{m}$Part $(\mathrm{b}) :$ When $\theta=10.9^{\circ},$ the torque equals 68.1 $\mathrm{N} \cdot \mathrm{m}$
Physics 102 Electricity and Magnetism
Chapter 22
Magnetism
Magnetic Field and Magnetic Forces
Sources of Magnetic field
Electromagnetic Induction
Inductance
Rutgers, The State University of New Jersey
University of Michigan - Ann Arbor
University of Washington
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so the formula for part eight to find the torque would be equaling and I a b sign of fatal. So here and is the number of turns in a loop and then four part and then I would be the current in the loop A is the essential of the cross sectional area of each turn into the loop and then be would be the magnitude of the magnetic field. And so we can say that here, in this case a is simply equaling the length of the side squared. And then we're going to say that then the area is equaling 18 centimeters or weaken. Say point 18 meters quantity squared. This is equaling 180.3 to 4 square meters and so we can say that here the maximum torque will be equaling. 150 turns in the loop, multiplied by the current of 50 0.0 amps multiplied by the area point 03 to 4 square meters, multiplied by the magnetic field of 1.60 Tesla's multiplied by sine of 90 degrees, which we know to be equaling one, and so the maximum torque is gonna be equaling 389 Newton meters. This would be our answer. Four part, eh? Four Part B. We're using the exact same formula and hear the torque is. The variables are exactly the same. The only thing that's changing is the angle. And so this would be the maximum torque or you can say not maximum at this point. But the torque would be equaling. 150 turns multiplied by 50.0 amperes, multiplied by 0.3 to 4 square meters, multiplied by 1.60 Tesla's time sign of 10.9 degrees. And so here. For part B, the torque is equaling 74 Newton meters. This would be our final answer for Part B. That is the end of the solution. Thank you for watching.
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