Question

Figure 2: 4. In Figure 2 point P is at the center of mass of a compass needle(m=0.002kg) and point O is the origin of the coordinate system. Consider a tiny compass needle[assumed to be a dipole] with a uniform magnetic moment $\vec{\mu} = (1, -1, 0)Am^2$ and with its center of mass located at $\vec{r}_m = (1, 1, 1)m$. The magnetic field vector is given by $\vec{B}_{ext} = (-x, -y, +2z)T/m$. The vector field $\vec{B}_{ext}$ is not shown. In torque calculations ignore the variation of the magnetic field over the dipole. (a) Determine the sum of the gravitational and magnetic potential energy and evaluate it at the center of the loop [gravitational force is assumed to be in z direction] $U_B + U_{mg} = $ (b) Determine the sum of the magnetic and gravitational force on the dipole $\vec{F}_B + \vec{F}_g = $ (c) Determine the sum of the magnetic and gravitational torque relative to the center of mass of the dipole and evaluate it at the center of the loop $\vec{\tau}^{(B)}_{cm} + \vec{\tau}^{(g)}_{cm} = $

          Figure 2:
4. In Figure 2 point P is at the center of mass of a compass needle(m=0.002kg) and point O is the origin of
the coordinate system. Consider a tiny compass needle[assumed to be a dipole] with a uniform magnetic moment
$\vec{\mu} = (1, -1, 0)Am^2$ and with its center of mass located at $\vec{r}_m = (1, 1, 1)m$. The magnetic field vector is given by
$\vec{B}_{ext} = (-x, -y, +2z)T/m$. The vector field $\vec{B}_{ext}$ is not shown. In torque calculations ignore the variation of the
magnetic field over the dipole.
(a) Determine the sum of the gravitational and magnetic potential energy and evaluate it at the center of the loop
[gravitational force is assumed to be in z direction]
$U_B + U_{mg} = $
(b) Determine the sum of the magnetic and gravitational force on the dipole
$\vec{F}_B + \vec{F}_g = $
(c) Determine the sum of the magnetic and gravitational torque relative to the center of mass of the dipole and
evaluate it at the center of the loop
$\vec{\tau}^{(B)}_{cm} + \vec{\tau}^{(g)}_{cm} = $

Figure 2:
4. In Figure 2 point P is at the center of mass of a compass needle(m=0.002kg) and point O is the origin of
the coordinate system. Consider a tiny compass needle[assumed to be a dipole] with a uniform magnetic moment
μ⃗ = (1, -1, 0)Am^2 and with its center of mass located at r⃗m = (1, 1, 1)m. The magnetic field vector is given by
B⃗ext = (-x, -y, +2z)T/m. The vector field B⃗ext is not shown. In torque calculations ignore the variation of the
magnetic field over the dipole.
(a) Determine the sum of the gravitational and magnetic potential energy and evaluate it at the center of the loop
[gravitational force is assumed to be in z direction]
UB + Umg =
(b) Determine the sum of the magnetic and gravitational force on the dipole
F⃗B + F⃗g =
(c) Determine the sum of the magnetic and gravitational torque relative to the center of mass of the dipole and
evaluate it at the center of the loop
τ⃗^(B)cm + τ⃗^(g)cm =

Added by Jennifer T.

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