Direction of Induced Currents in Coplanar Wire Segments

To determine the magnitude and direction of the induced currents $I_1$ and $I_2$, we apply Faraday's Law and Lenz's Law:

1. Current Magnitude:
   The wire segments are connected in series to form a single continuous coplanar loop. By the conservation of charge (Kirchhoff's Current Law), the current must be uniform throughout the entire loop. Therefore:
   $I_1 = I_2$
   Hence, options (A) and (B) are incorrect.

2. Current Direction:

   • The magnetic field $\mathbf{B}$ is directed perpendicularly into the plane of the loop ($\otimes$) and its magnitude is increasing with time ($\frac{dB}{dt} > 0$).
   • According to Lenz's law, the induced current must flow in a direction such that the induced magnetic field opposes the increase in inward magnetic flux. Therefore, the induced magnetic field must be directed perpendicularly out of the plane ($\odot$).
   • To produce an outward magnetic field, the net circulation of current around the outer boundary of the loop must be counter-clockwise.
   • Along the outer boundary, a counter-clockwise circulation means the current flows:
     • Right-to-left along the top segment $\mathbf{cd}$, which is in the direction from $\mathbf{d}$ to $\mathbf{c}$ ($\mathbf{dc}$).
   • Along the inner segment $\mathbf{ab}$, the current flows in the opposite direction (from left to right) to complete the loop, which corresponds to the direction from $\mathbf{a}$ to $\mathbf{b}$ ($\mathbf{ab}$).

Thus, $I_1$ is in the direction $\mathbf{ab}$ and $I_2$ is in the direction $\mathbf{dc}$.

Therefore, the correct option is D.