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# A short bar magnet of magnetic moment $0.4J/T$ is placed in a uniform magnetic field of $0.16T$. The magnet is in stable equilibrium when the potential energy is

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## Step 1: Given dataThe magnetic moment of the bar is ${p}_{m}=0.4J/T.$The magnitude of the uniform magnetic field $B=0.16T.$Step 2: The potential energy of a bar magnetThe potential energy stored in a bar magnet when it is placed in a magnetic field is the vector dot product of the magnetic moment and magnetic field.The potential energy of a magnet is defined by the form, $U=-\stackrel{\to }{{P}_{m}}.\stackrel{\to }{B}$, where, ${P}_{m}$ is the magnetic moment and $B$ is the magnitude of a magnetic field.The magnet will be in stable equilibrium when the bar magnet is aligned along the magnetic field. In this stable equilibrium, the potential energy will be minimum.Step 3: DiagramStep 4: Finding the potential energyAs we know, the potential energy of a magnet in a magnetic field is $U=-\stackrel{\to }{{P}_{m}}.\stackrel{\to }{B}$So, $U=-\stackrel{\to }{{P}_{m}}.\stackrel{\to }{B}={p}_{m}×B×\mathrm{cos}\theta$At stable equilibrium, $\theta =0$ ( the bar magnet is aligned along the magnetic field)Now, $U={p}_{m}×B×\mathrm{cos}\theta =\left(0.4\right)×\left(0.16\right)×\mathrm{cos}0\phantom{\rule{0ex}{0ex}}orU=0.064×1\phantom{\rule{0ex}{0ex}}orU=0.064J.$Therefore, the potential energy when the magnet is in stable equilibrium is $0.064joule.$

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