A coil is placed in a magnetic field $$\vec{B}$$ as shown below:

A current is induced in the coil because $$\vec{B}$$ is:

We need to determine the correct physical state of the magnetic field $$\vec{B}$$ that causes the indicated counter-clockwise induced current in the circular coil based on the principles of electromagnetic induction.

1. Identify the Direction of the Induced Magnetic Field

According to the diagram, the induced current in the coil flows in a counter-clockwise (anti-clockwise) direction.

Using the Right-Hand Thumb Rule (curl the fingers of your right hand in the direction of the counter-clockwise current), your thumb points straight out of the page. This means the induced magnetic field ($$\vec{B}_{\text{induced}}$$) created by this current is directed outward (towards the viewer).

2. Apply Lenz's Law

Lenz's Law states that the direction of an induced current will always be such that it opposes the change in magnetic flux that produced it:

• If the original magnetic field $$\vec{B}$$ is directed outward and its magnitude is decreasing with time, the magnetic flux through the loop is dropping. To oppose this reduction, the coil induces a magnetic field in the same direction (outward) to sustain the flux.
• If the original magnetic field $$\vec{B}$$ was outward and increasing, the loop would try to oppose the growth by creating an inward field (which would cause a clockwise current).

Since the induced field points outward to reinforce the system, the external magnetic field $$\vec{B}$$ must be outward and decreasing with time.

3. Match with the Options

This matches the physical scenario where the magnetic field vector points outward perpendicular to the loop area while dropping in intensity over time.

Correct Option: C (outward and decreasing with time)