We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. There is one last feature of dipoles we need to address – how they react to non-uniform fields. This is then used to find the change in gravitational PE: \[\Delta y = r\theta = \left(0.25\;m\right)\left(\dfrac{\pi}{2}\right) = 0.39\;m\;\;\;\Rightarrow\;\;\; \Delta U_{grav} = mg\Delta y = \left(0.45\;kg\right)\left(9.8\;\frac{m}{s^2}\right)\left(0.39\;m\right) = 1.7\;J\nonumber\]. Write the definition of magnetic dipole moment. and Differentiability. CBSE likely to conduct the class 12 & class 10 board exam 2021 earlier than expected. trailer 0000005261 00000 n Consider an electric dipole in an electric field that gets stronger along a specific direction. Let θ be the angle between the magnetic dipole direction and the external field direction. %%EOF For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. The magnetic moment starts at an angle of 90º with the field, and ends at an angle of 0º: \[\Delta U_{mag} = \left(-\mu B \cos 0^o\right) - \left(-\mu B \cos 90^o\right) = -IAB = -I \left(0.54\;m\right)^2\left(1.2\;T\right) = -I\left(0.35\;Tm^2\right)\nonumber\]. A magnetic dipole is situated in the direction of a magnetic field. So we have the potential energy of a dipole in a field: \[U_{electric} = -\overrightarrow p \cdot \overrightarrow E \;\;\;\Leftrightarrow\;\;\; U_{magnetic} = -\overrightarrow \mu \cdot \overrightarrow B\]. Arham qualifying the Microsoft certification exam at Pearson VUE test centre. Check BSEB sent up exam 2021 time table, sent up exam paper pattern, & other details. 0000006938 00000 n [ "article:topic", "authorname:tweideman", "license:ccbysa", "showtoc:no" ]. At the top of its journey the mass gains gravitational potential energy, and this must have come from the magnetic potential energy of the dipole in the field. Since magnetic sources are inherently dipole sources which can be visualized as a current loop with current I and area A, the energy is usually expressed in terms of the magnetic dipole moment: The device shown in the diagram consists of a square loop through which flows a steady current, located in a uniform magnetic field, and attached to an axle that turns a wheel. The direction is trickier to come up with, but blowing up the picture and doing a bit of geometry, we can determine its components: Figure 4.2.3 – Writing the Current Element Vector. 0000001964 00000 n max µΒ! Calculate potential energy of a magnetic dipole in a magnetic field. 0000026050 00000 n 0 What is magnetic dipole moment? %PDF-1.4 %���� 0000026669 00000 n Expressions and Identities, Direct 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.
Reason: Force would also acts on dipole if magnetic field were uniform.

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