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A wire loop enclosing a semi-circle of radius \( a=2 \mathrm{~cm} \) is located on the boundary of a uniform magnetic field of induction \( B=1 \mathrm{~T} \) (figure). At the moment \( t=0 \) the loop is set into rotation with a constant angular acceleration \( \beta=2 \mathrm{rad} / \sec ^{2} \) about an axis \( O \) coinciding with a line of vector \( B \) on the boundary. The emf induced in the loop as a function of time \( t \) is \( \left[x \times 10^{-4}(-1)^{n} \times t\right] \) volts, where \( n=1,2, \ldots \) is the number of the half-revolution that the loop performs at the given moment \( t \). Find the value of \( x \). (The arrow in the figure shows the emf direction taken to be positive, at \( t=0 \) loop was completely outside)
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