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That is, we have the makings of an electric motor. I am not understanding why the potential energy (U) for a magnetic dipole is at it's maximum when the magnetic dipole moment is antiparallel to the magnetic field (B), why U is at it's minimum when the magnetic dipole moment and B are parallel, and why U is zero when B and the magnetic dipole moment are perpendicular. Now use energy conservation to solve for the current: \[0=\Delta U_{grav} +\Delta U_{mag}+\Delta KE = 1.7J -I\left(0.35\;Tm^2\right) + 0 \;\;\;\Rightarrow\;\;\; I = \dfrac{1.7\;J}{0.35\;Tm^2} = 4.9\;A\nonumber\]. choose the axes so that \(\widehat i \times \widehat j = \widehat k\)), select an infinitesimal piece os the loop, and describe it in terms of the coordinates, labeling whatever variables we will need to know along the way. Magnetic Potential Energy. Know UK board 2021 exam date sheet & others details here. Assertion: When a magnetic dipole is placed in a non uniform magnetic field, only a torque acts on the dipole. The quantity \(yz\) is the area of the loop, \(A\). These forces act straight through the axis, so the torque they produce is zero. Consider an electric dipole in an electric field that gets stronger along a specific direction. Check BSEB sent up exam 2021 time table, sent up exam paper pattern, & other details. Calculate the change in magnetic dipole moment when the electron in a atom makes a transition from the orbit to the orbit. If it is rotated by, Calculate the change in magnetic dipole moment when the electron in a, The torque acting on a magnetic dipole of moment, CBSE Scholarship for Single Girl Child - More Power to Girls. Have questions or comments? Legal. to Euclids Geometry, Areas %���� 0000004119 00000 n
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To find the torque vector, we first need the magnetic moment. 0000040919 00000 n
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So we have the potential energy of a dipole in a field: \[U_{electric} = -\overrightarrow p \cdot \overrightarrow E \;\;\;\Leftrightarrow\;\;\; U_{magnetic} = -\overrightarrow \mu \cdot \overrightarrow B\]. You have noted that it is a dot product. 0000001964 00000 n
The torque direction comes from the cross product of magnetic moment and field. 0000011246 00000 n
If the magnetic field is unchanging, then the rotation of the magnetic moment will cause the torque to reverse direction, which means the torque cause the loop to accelerate the opposite direction. Find the torque (vector) exerted on the conductor. 39 39
Potential Energy of magnetic dipole in magnetic field is defined as the amount of work done in rotating the dipole from zero potential energy position to any desired position.. A current loop does not experience a net force in a magnetic field. And the derivation of required formula… the loop does not spin all the way around, but rather goes back-and-forth). colleges and universities in the state. JEE Main 2021 preparation tips, strategies & marking scheme. 0000066860 00000 n
Reason: Force would also acts on dipole if magnetic field were uniform.
Reason: Force would also acts on dipole if magnetic field were uniform. Besides, the direction of magnetic field lines in the direction of your curled fingers. Meet 6-Year-Old Ahmedabad Boy World’s Youngest Computer Programmer. 39 0 obj <>
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This consists of a ring with a break in it that rotates inside two rubbing connections. Write the definition of magnetic dipole moment. to Three Dimensional Geometry, Application The torque and magnetic potential energy of a magnetic dipole in most stable position ina uniform magnetic field. Choosing the positive torque direction to be to the left, the forces on top and bottom both generate torques in that positive direction, so: \[\tau_{net} = F_{top}\left(\dfrac{z}{2}\right) + F_{bottom}\left(\dfrac{z}{2}\right) = 2\left(IyB\right)\left(\dfrac{z}{2}\right) = I\left(yz\right)B\]. a. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. For example, the force on the current element is: \[d\overrightarrow F = I \overrightarrow {dl} \times \overrightarrow B = I\left[R\;d\phi\left(-\sin\phi\;\widehat i + \cos\phi\;\widehat j\right)\right]\times\left[B \;\widehat i\right]\]. ˆr r2 (r from q to m ). (10) In this, r points fromq to m . x�b```f``ia`c`�\� �� �@Q��(�7V6>6FF���9,�Y��7]}�~k�,��Iƈ�`�˧�i���oH�8t�b�?���3 ��������?�89
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The usual convention for the interaction potential energy We will choose a simple geometry for this analysis – a rectangular loop of wire with two sides parallel to a uniform magnetic field. We calculate that to be (use RHR for direction): \[\overrightarrow \mu = IA\left(-\widehat k\right) = \left(2.00A\right)\pi\left(0.12m\right)^2\left(-\widehat k\right) = \left(-9.05\times 10^{-2} A\cdot m^2\right)\widehat k\nonumber\]. and Inverse Proportions, Areas Algebraic This makes the coil oscillate back-and-forth, rather than rotate in a single direction. Try it now. Uttarakhand CM Announces Free WI-FI Service in all Govt. As per the law of conservation of energy, since the work done on the object is equal to m×g×h, the energy gained by the object = m×g×h, which in this case is the potential energy E.. E of an object raised to a height h above the ground = m×g×h. bhi. It however, experiences a torque. Sure enough, the magnitude of the torque comes out to be \(\mu\;B\), where \(\mu=IA\). CBSE scholarship for single girl child to the deserving candidates, who are the only child of their parents. To get the torque, we choose the origin as a reference point, and compute the infinitesimal contribution to the torque directly. 0000004374 00000 n
\[g = 9.8\;\frac{m}{s^2} \;,\;\;\; m=0.45\;kg\;,\;\;\; B=1.2\;T\;,\;\;\; \text{length of the sides of the loop} = 0.54m\;,\;\;\; \text{radius of wheel} = 0.25m\nonumber\]. (\376\377\000P\000i\000n\000g\000b\000a\000c\000k\000s) Know how to apply, dates, eligibility, amount & more. What is magnetic dipole moment? By creating a torque in a conducting loop that carries a current, we can have it do work. to Trigonometry, Complex %PDF-1.5 One way to fix this is to provide an emf that switches direction periodically, so that the current flips when the magnetic moment is about to provide the wrong torque. 0000001787 00000 n
Choosing an axis that is a horizontal line passing through the centers of the two vertical segments, we can compute the net torque on the loop. 0! When is potential energy of a magnetic dipole minimum? 0000007513 00000 n
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When the loop rotates around the horizontal axis, the angle between the magnetic dipole moment and the field changes, reducing the moment arms of the forces by a factor of \(\sin\theta\) – exactly the amount accounted-for in the cross-product. and Differentiability. 0000008175 00000 n
Magnetic Dipole Moment: Potential Energy But when the field is not uniform, then half of the dipole can be in a region where the field is stronger than the region where the other half of the dipole is, resulting in more force on one part of the dipole than the other, and a net force on the dipole as a whole. _��(�w���̧�s�ͳ�pff��_F�����ٕ�-|�TԕU��Z�"���l������Y�'7�����L�4-�z���h73_�E��it{���
/��V�����r�쬒DTZߑ·��k�fd(v��'�7��}t\R�_q�9�8p.&'�Z�|f�\e�u����T�0)�IMt���oZP��S�m`�}�. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. endobj It is useful to make the direct comparison of these two dipoles in their respective fields with a diagram. And it seems to me U would be zero when the dipole moment is parallel or antiparallel to B because when the dipole is in this position there is no potential for the dipole to rotate, the torque is zero when the dipole is at the positions. 0000006533 00000 n
The horizontal sides of the rectangular loop are perpendicular to the field, so the sine of the angle that appears in the cross-product is exactly equal to one. Meet 6-year-old Ahmedabad boy World’s youngest computer programmer. Magnetic Dipole In Uniform Magnetic Field. The product of \(N\), \(I\), and \(A\) is written as a single quantity \(\mu\), giving the magnitude of the torque for this case the simple form of \(\tau = \mu B\). Is is clear that the potential energy U(θ) of a magnetic dipole moment in a magnetic field is given by, Study reveals how to improve natural gas production in shale, Researchers make key advance for printing circuitry on wearable fabrics, Weather-proof chip aims to take self-driving tech, wireless communications to next level, http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magpot.html, http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html, Potential Energy for dipole in Electric Field, Potential Energy of Dipole in Electric Field, Deriving the energy of a magnetic dipole in a magnetic field, Frame of reference question: Car traveling at the equator, Seeking a simple logical argument to an interesting statement (spring-mass motion), Determining the starting position when dealing with an inclined launch. Find the formula for the moment of force on a magnetic dipole located in the same magnetic field. << /S /GoTo /D (section*.1) >> Figure 4.2.1 – Closed Rectangular Loop of Wire in a Uniform Magnetic Field. 0000002593 00000 n
For a better experience, please enable JavaScript in your browser before proceeding. Suppose that the atoms is in a magnetic field of induction. 12 0 obj 0000004450 00000 n
Colleges. CBSE Board Exams 2021 Could be Held Early, Know the Reason. What is the energy difference between the highest and the lowest state? dipole in an electric field, we can work out the energy of a magnetic dipole in a magnetic field. Curling our fingers counterclockwise gives this direction, so that is the direction of the current. Figure 4.2.2a – Torque on a Closed Circular Loop of Wire in a Uniform Magnetic Field. When the loop rotates to the point where its plane is perpendicular to the field, the magnetic moment and field are parallel, making the torque zero, as we found above. Missed the LibreFest? trailer
The system conserves energy, and the mass is moving at neither the top nor the bottom of its journey, so the kinetic energy doesn’t change. The force on the top and bottom segments must be perpendicular to the field, so there are horizontal components of this force that add together, and vertical parts that cancel, the net force being to the right, just as it is in the analogous case for the electric dipole. All that remains is to add up all of the torque contributions, which means integrating over the angle \(\phi\) from \(0\rightarrow 2\pi\): \[\overrightarrow \tau =-IR^2B\int\limits_0^{2\pi}d\phi\left[\cos^2\phi \left(-\widehat j\right) + \sin\phi \cos\phi \left(\widehat i\right)\right] = IR^2B\left[\pi \;\widehat j-0 \;\widehat i\right]=I\left(\pi R^2\right)B\;\widehat j\]. The magnetic field is uniform, and the current doesn’t change direction, so combining this with the previous observation, we get a force on each of these segments equal to the same value: \(IyB\). Watch the recordings here on Youtube! A magentic dipole in a constant magnetic field has, In the potential energy of magnetic dipole is zero when, What is the expression for potential energy of a dipole of moment M held at an angle. The torque exerted by a field on a dipole is N=m B (1) If we bring in a dipole from infinity in such a way that no work is done (by moving the dipole along a path that is always perpendicular to the force