A circular loop of wire with radius \( r \), weighing \( m \) kilograms, carries a steady current of \( I \) amperes. The loop's axis is constrained to remain perpendicular to a large planar sheet of a perfect conductor. The loop is free to move vertically, and its instantaneous height is \( a \) meters. It is moving at a speed \( v \) in the y-direction, where \( v \ll c \).
Calculate the approximate equilibrium height \( x \) and the frequency of small vertical oscillations for a current value where \( r \ll x \).
1
\( \omega_0 = \sqrt{\frac{\mu_0 I^2 r}{4 m x^2}} \)
2
\( \omega_0 = \sqrt{\frac{\mu_0 I^2 r}{2 \pi m x^2}} \)
3
\( \omega_0 = \sqrt{\frac{\mu_0 I^2 r}{2 m x^2}} \)
4
\( \omega_0 = \sqrt{\frac{\mu_0 I^2 r}{4 \pi m x^2}} \)