(T/F) 1. The torque on a magnetic dipole has its largest valuewhen the dipole is
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Question
(T/F) 1. The torque on a magnetic dipole has its largest valuewhen the dipole is oriented at 180deg with respect to the magneticfield exerting the torque. 2. The magnetic potential energy of a magnetic dipolehas its largest value when the magnetic dipole moment is orientedat 180deg relative to the magnetic field. 3. The magnetic moment of a current-carrying loopdepends on the current and the area enclosed by the loop. 4. Consider the relationships between the directions ofthe torque acting on a magnetic dipole in a magnetic field, themagnetic field, and the magnetic dipole moment. The torque isparallel to the magnetic field, but perpendicular to the dipolemoment. 5. A magnetic dipole has two stable orientations in amagnetic field: these are when the loop is oriented at 90deg and270deg with respect to the field.A magnetic dipole has two stable orientations in a magnetic field:these are when the loop is oriented at 90deg and 270deg withrespect to the field. (T/F) 1. The torque on a magnetic dipole has its largest valuewhen the dipole is oriented at 180deg with respect to the magneticfield exerting the torque. 2. The magnetic potential energy of a magnetic dipolehas its largest value when the magnetic dipole moment is orientedat 180deg relative to the magnetic field. 3. The magnetic moment of a current-carrying loopdepends on the current and the area enclosed by the loop. 4. Consider the relationships between the directions ofthe torque acting on a magnetic dipole in a magnetic field, themagnetic field, and the magnetic dipole moment. The torque isparallel to the magnetic field, but perpendicular to the dipolemoment. 5. A magnetic dipole has two stable orientations in amagnetic field: these are when the loop is oriented at 90deg and270deg with respect to the field.
A magnetic dipole has two stable orientations in a magnetic field:these are when the loop is oriented at 90deg and 270deg withrespect to the field.
Explanation / Answer
1) Torque on a magnetic dipole is given by: = m xB where m is the magnetic dipole moment. So the magnitude can be found as: = mBsin where is the angle between the dipole moment and themagnetic field. If is 180 degrees, then sin = 0 (whichis 0 torque). This is clearly not the maximum: sin is maximized at 1, whichoccurs when = 90 degrees. (1) is false 2) The potential energy is equal to the amount of work done on thedipole until it reaches equilibrium ( = 0). In other words,if I were to put a dipole moment oriented in such a fashion suchthat it will have torque, it's potential energy is equal to theamount of work that was needed to rotate the dipole moment into astable position ( = 0). If we want to maximize potential energy, we need to maximize theinitial torque (because the system will continue to act to reducetorque, or minimize energy). We just found that the system hasmaximum torque at 90 degrees, so (2) is false. 3) The magnetic dipole moment is defined as: m = IA where I is the current and A is the area of the loop. So(3) is true by definition. 4) Again, consider the definition of the torque of a dipolemoment: = m xB If you recall your vector calculus, the resultant vector of a crossproduct must be perpendicular to both vectors in the crossproduct (this is why we use the right hand rule to find thedirection of the vector). So (4) is false. 5) The stable orientations occur when torque = 0. Earlier we found that this was the case when sin = 0. Whendoes sin = 0? At 0 degrees, 180 degrees, or 360 degrees.Not at 90 or 270 degrees (these would produce 1 and -1respectively). So it cannot be that these are stableconfigurations. Therefore (5) is false.
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