Choose the correct sketch of the magnetic field lines of a circular current loop shown by the dot and the cross $$\otimes$$.

To solve this problem, we need to determine the correct sketch of the magnetic field lines for a circular current loop. The loop is shown with a dot and a cross, which represent the direction of the current. The dot (•) indicates current coming out of the plane (towards the viewer), and the cross (×) indicates current going into the plane (away from the viewer). We must recall the pattern of magnetic field lines around a current-carrying loop and apply the right-hand thumb rule to find the direction of the magnetic field.

First, visualize the circular loop lying in the plane of the paper. The dot is at one point on the loop, and the cross is at the opposite point. This means the current flows from the dot (coming out) to the cross (going in) along the circular path. If we consider the dot at the top and the cross at the bottom, the current flows clockwise when viewed from above. To confirm, imagine moving from the top: the current comes out (dot), flows to the right, then down, then to the left at the bottom (going in, cross), and back up to complete the loop. Thus, the current is clockwise.

Next, apply the right-hand thumb rule to find the direction of the magnetic field at the center of the loop. Curl the fingers of your right hand in the direction of the current (clockwise). Your thumb will point downward, into the plane of the paper. Therefore, the magnetic field at the center is directed into the paper, represented by crosses (×).

Now, recall the general pattern of magnetic field lines for a circular current loop. The field lines form closed loops around the current. Near the center, they are nearly straight and perpendicular to the plane of the loop. As we move away from the center, they curve and spread out. The loop behaves like a magnetic dipole: one side acts as a north pole (from which field lines emerge), and the opposite side acts as a south pole (into which field lines enter). For a clockwise current, the magnetic field at the center is into the paper, so the top face (where the dot is) is the south pole (field lines enter), and the bottom face (where the cross is) is the north pole (field lines emerge). Thus, above the loop (along the axis), the field lines are directed into the paper (crosses), and below the loop, they are directed out of the paper (dots). The field lines curve around the sides, forming continuous loops from the bottom (north pole) to the top (south pole).

With this understanding, examine the options:

Option A (Diagram 1): Shows field lines with crosses (into the paper) inside the loop and above the loop, and dots (out of the paper) below the loop. The lines form closed loops curving from the bottom (dots) around to the top (crosses). This matches the pattern for a clockwise current.

Option B (Diagram 2): Shows dots (out of the paper) inside the loop and above the loop, and crosses (into the paper) below the loop. This would correspond to a counterclockwise current, which is opposite to our case.

Option C (Diagram 3): Shows field lines that are circular and concentric but do not correctly represent the dipole-like pattern. The directions are inconsistent with the current flow.

Option D (Diagram 4): Shows field lines that are not symmetric and do not align with the expected behavior for a circular loop. The directions do not match the required pattern.

Therefore, Diagram 1 (Option A) correctly depicts the magnetic field lines for the given circular current loop with clockwise current.

Hence, the correct answer is Option A.