There is a uniform magnetic field directed perpendicular and into the plane of the paper. An irregular shaped conducting loop is slowly changing into a circular loop in the plane of the paper. Then

Options

A. current is induced in the loop in the anti-clockwise direction
B. current is induced in the loop in the clockwise direction
C. AC is induced in the loop
D. No current is induced in the loop

Explanation

To solve the problem, we need to analyze the situation step by step:

### Step 1: Understand the Magnetic Field
The problem states that there is a uniform magnetic field directed perpendicular and into the plane of the paper. This means that the magnetic field lines are pointing towards the observer (represented by crosses in diagrams).

**Hint:** Visualize the magnetic field direction; it helps in understanding how it interacts with the loop.

### Step 2: Analyze the Conducting Loop
We have an irregularly shaped conducting loop that is changing into a circular loop. As the shape of the loop changes, the area of the loop is also changing.

**Hint:** Remember that the area of the loop is crucial because it affects the magnetic flux through the loop.

### Step 3: Determine the Change in Area
As the irregular loop transforms into a circular loop, the area of the loop increases. This increase in area leads to a change in magnetic flux through the loop.

**Hint:** Recall the formula for magnetic flux: \( \Phi = B \times A \), where \( B \) is the magnetic field strength and \( A \) is the area of the loop.

### Step 4: Apply Faraday's Law of Electromagnetic Induction
According to Faraday's Law, a change in magnetic flux through a loop induces an electromotive force (emf) in the loop. The induced emf will generate a current in the loop.

**Hint:** Faraday's Law states that the induced emf is proportional to the rate of change of magnetic flux.

### Step 5: Determine the Direction of Induced Current
Lenz's Law states that the direction of the induced current will be such that it opposes the change in magnetic flux. Since the area of the loop is increasing, the magnetic flux through the loop is also increasing.

- The magnetic field is directed into the paper, and since the flux is increasing in this direction, the induced current must create a magnetic field that opposes this increase.
- To oppose the increase in flux (which is into the paper), the induced current must flow in an anticlockwise direction (as viewed from above).

**Hint:** Use the right-hand rule to determine the direction of the induced current based on the direction of the magnetic field and the change in flux.

### Step 6: Conclusion
The induced current in the loop is in the anticlockwise direction.

**Final Answer:** The current induced in the loop is in the anticlockwise direction.