A rectangular current loop (magnetic moment m=IA) is placed in a uniform external magnetic field B. For what orientation of the loop is it in (1) stable equilibrium and (2) unstable equilibrium?

PhysicsMediumHigh School (11–12)jee-main

The potential energy of a magnetic dipole in a field is $U=-\vec{m}\cdot\vec{B}=-mB\cos\theta$ , where $\theta$ is the angle between $\vec{m}$ and $\vec{B}$ . $U$ is minimum (stable) when $\vec{m}\parallel\vec{B}$ ( $\theta=0$ ) and maximum (unstable) when $\vec{m}$ is antiparallel to $\vec{B}$ ( $\theta=180°$ ).

A rectangular current loop (magnetic moment $\vec{m}=I\vec{A}$ ) is placed in a uniform external magnetic field $\vec{B}$ . For what orientation of the loop is it in (1) stable equilibrium and (2) unstable equilibrium?

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← A current-carrying loop lies in the xy-plane, shaped as shown in a standard textbook figure: it consists of a square loop of side a with two semicircular lobes of radius a attached on opposite sides, with current I flowing around the loop in a sense such that the unit vector k̂ (out of the page) gives the direction of the magnetic moment. What is the magnetic moment of this current loop?A conducting wire bent into the shape of the parabola y² = 2x carries a current i = 2 A, from point B(2,-2) to point A(2,2) (coordinates in metres), as shown in the figure. This wire lies in a uniform magnetic field B = -4k̂ tesla (field is uniform everywhere, directed into the page). What is the magnetic force on the wire? →

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