Final answer:
The change in magnetic flux depends on the motion of the charged particle. If there's no relative motion or changing magnetic field caused by the charge, the magnetic flux remains constant. If the particle's motion induces a changing magnetic field, the flux changes and a current might be induced in the loop.
Step-by-step explanation:
The question addresses the change in magnetic flux through a loop when a positively charged particle with twice the initial charge is placed to the left of the loop. Magnetic flux is defined as the product of the magnetic field and the area through which the field is passing, and it measures how many magnetic field lines are passing through the loop.
As the charge to the left of the loop is increased, the electric field around the charge likewise increases, but this does not directly affect the magnetic flux unless there is relative motion between the charge and the loop, or unless the charge's motion itself generates a changing magnetic field.
If the positively charged particle is stationary or moving uniformly, it will not change the magnetic flux through the loop, as there are no changing magnetic field lines crossing the loop. Hence, the magnetic flux through the loop would remain constant.
However, if the charged particle is moving with a changing velocity, then according to electromagnetic induction principles, this could induce a changing magnetic field. If the motion of the charged particle affects the magnetic field through the loop, then the induced magnetic field due to the particle would have to be into the page to oppose the increase according to Lenz's Law, resulting in a clockwise current as per the right-hand rule.
In this scenario, there would be a change in magnetic flux, but the specific nature of flux change isn't provided in the details, so the exact answer choice from the options would depend on additional context about the charge's motion.