Figure 4.2.6 – Net Force on an Magnetic Dipole from a Non-Uniform Field. $\overrightarrow{ M }= m (\overrightarrow{2 \ell})$ Important Points to Remember (1) It is a vector quantity whose direction is from south pole to north pole of magnet. Here are the main features of this set-up: The forces on the horizontal segments cancel, resulting in zero net force on the loop, but of course there is a net torque. (To date, no isolated magnetic monopoles have been experimentally identified.) Then the demagnetizing portion of H does not include, by description, the part of H {\displaystyle \mathbf {H} }due to free currents, there occurs a magnetic scalar potential such that, In the amperian loop model, the related magnetic field is the magnetic induction B{\displaystyle \mathbf {B} }. Figure 4.2.2a – Torque on a Closed Circular Loop of Wire in a Uniform Magnetic Field. At the present, if we think a point which is far from the current loop such that l>>R, then we can estimate the field as: \[B = \frac{\mu_{0}i R^{2}}{2l^{3}((\frac{R}{i})^{2} + 1)^{\frac{3}{2}}} \approx \frac{\mu_{0}i R^{2}}{2l^{3}} = \frac{\mu_{0}}{4\pi} \frac{2i(\pi R^{2})}{l^{3}}\], therefore, the magnetic field can be written as, \[B = \frac{\mu_{0}}{4\pi} \frac{2iA}{l^{3}} = \frac{\mu_{0}}{4\pi} \frac{2\mu}{l^{3}}\], We can mark this new quantity μ as a vector which points next to the magnetic field, so that, \[\overrightarrow{B} = \frac{\mu_{0}}{4\pi} \frac{2 \overrightarrow{\mu}}{l^{3}}\]. b. The torque vector can now be calculated from the magnetic dipole moment in the same way that the torque exerted on an electric dipole was calculated: \[\overrightarrow\tau_{electric} = \overrightarrow p \times \overrightarrow E \;\;\;\Leftrightarrow\;\;\; \overrightarrow\tau_{magnetic} = \overrightarrow \mu \times \overrightarrow B\]. The magnetic field between both poles (see figure for Magnetic pole definition) is in the opposite direction to the magnetic moment (which points from the negative charge to the positive charge), while within a current loop it is in the same direction (see the figure to the right). For a current loop, this definition hints to the magnitude of the magnetic dipole moment corresponding to the product of the current times the region of the loop. Here we introduce a shortcut for future torque calculations. Next calculate the potential energy change of the dipole in the field in terms of the current. The force between two magnetic poles in air is 9.604 mN. Pro Lite, Vedantu The denominators of this equation can be prolonged with the help of multipole expansion to give a sequence of terms that have greater power of distances in the denominator. There is one last feature of dipoles we need to address – how they react to non-uniform fields. (2) The line joining the poles of the magnet is called magnetic axis. Download India's Leading JEE | NEET | Class 9,10 Exam preparation app, Magnetic Dipole Moment Definition, Formulas & Solved Examples | Class 12, JEE & NEET, (2) The line joining the poles of the magnet is called, (3) The distance between the two poles of a bar magnet is called the, (4) The distance between the ends of the magnet is called, Magnetic Field | Properties of Magnetic Lines of Force Class 12, JEE, JEE Main Previous Year Questions Topicwise, Ferromagnetic Substance – Magnetism & Matters | Class 12 Physics Notes, Paramagnetic Substances – Magnetism & Matters | Class 12 Physics Notes, Forces || Newton Laws Of motion || Class 11 Physics Notes, JEE Main Guided Revision Test Series (For Jan 2021 Attempt) Syllabus & Schedule, Class 12 CBSE Sample Question Papers 2021. We found that we could do more with electric dipoles than just compute torques, and the same is true for magnetic dipoles. is the vector cross product, In the magnetic pole perspective, and the first non-zero term of the scalar potential is. Save my name, email, and website in this browser for the next time I comment. Here r is the position vector, j is the electric current density & the integral is a volume integral. The quantity \(yz\) is the area of the loop, \(A\). If m is the pole strength then M = m . Here m may be represented in terms of the magnetic pole strength density but is more usefully expressed in terms of the magnetization field as: The same symbol m is used for both equations since they produce equivalent results outside of the magnet. (1) Two poles of a magnetic dipole or a magnet are of equal strength and opposite nature. We know that torque and magnetic field are both vectors, and the torque created is related to the orientation of the loop in the field. New magnetic dipole moment M’ = m’ $(2 \ell)=\frac{ m }{2} \times 2 \ell=\frac{ M }{2}$.