A square wire frame (initially current is zero) with side \( a \) and a straight conductor carry...

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A square wire frame (initially current is zero) with side \( a \) and a straight conductor carrying a constant current \( I \) are located in the same plane (figure). The inductance and the resistance of the frame are equal to \( L \) and \( R \) respectively. The frame was turned through \( 180^{\circ} \) about the axis \( O O^{\prime} \) separated from the current-carrying conductor by a distance \( b=2 a \). The total electric charge having flown through the frame if \( i=0 \) at \( t=0 \) in the loop is equal to \( \frac{\mu_{0} a I}{2 \pi R} \ln x \). Find the value of \( x \).
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