Question

Y1401 The magnetic field at a field point \textbf{r} due to a magnetic dipole \textbf{\mu} is \textbf{B} = \frac{\mu_0}{4\pi} \left[ \frac{3\textbf{r}(\textbf{\mu} \cdot \textbf{r})}{r^5} - \frac{\textbf{\mu}}{r^3} \right] The unit vectors \hat{\textbf{e}}_1, \hat{\textbf{e}}_2, \hat{\textbf{e}}_3 and the red circular wire C of radius \rho are fixed. The magnet of dipole moment \textbf{\mu} rotates with the time dependence \textbf{\mu}(t) = \mu(\hat{\textbf{e}}_3 \cos \omega t + \hat{\textbf{e}}_2 \sin \omega t). The distance between the magnet center at the origin O and the circle center P is D. Compute the following quantities in the limit D >> \rho, d. A Magnetic flux passing the inner surface of C in the direction of \hat{\textbf{e}}_3. B The potential increment after making a single round trip from Q to the same point along the direction. C The power consumed by the wire if the resistance of C is R.

          Y1401
The magnetic field at a field point \textbf{r} due to a magnetic dipole \textbf{\mu} is
\textbf{B} = \frac{\mu_0}{4\pi} \left[ \frac{3\textbf{r}(\textbf{\mu} \cdot \textbf{r})}{r^5} - \frac{\textbf{\mu}}{r^3} \right]
The unit vectors \hat{\textbf{e}}_1, \hat{\textbf{e}}_2, \hat{\textbf{e}}_3 and the red
circular wire C of radius \rho are fixed.
The magnet of dipole moment \textbf{\mu}
rotates with the time dependence
\textbf{\mu}(t) = \mu(\hat{\textbf{e}}_3 \cos \omega t + \hat{\textbf{e}}_2 \sin \omega t).
The distance between the magnet
center at the origin O and the circle
center P is D. Compute the following
quantities in the limit D >> \rho, d.
A Magnetic flux passing the inner surface of C in the direction of \hat{\textbf{e}}_3.
B The potential increment after making a single round trip from Q
to the same point along the direction.
C The power consumed by the wire if the resistance of C is R.

Y1401
The magnetic field at a field point r due to a magnetic dipole μ is
B = (μ0)/(4π) [ (3r(μ ·r))/(r^5) - (μ)/(r^3) ]
The unit vectors ê1, ê2, ê3 and the red
circular wire C of radius ρare fixed.
The magnet of dipole moment μ
rotates with the time dependence
μ(t) = μ(ê3 cosωt + ê2 sinωt).
The distance between the magnet
center at the origin O and the circle
center P is D. Compute the following
quantities in the limit D >> ρ, d.
A Magnetic flux passing the inner surface of C in the direction of ê3.
B The potential increment after making a single round trip from Q
to the same point along the direction.
C The power consumed by the wire if the resistance of C is R.

Added by Alejandra G.

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