A circular loop of flexible conducting material is kept in a magnetic field directed perpendicularly into its plane. By holding the loop at diametrically opposite points its is suddenly stretched outwards, then

Options

A. No current is induced in the loop
B. Anti-clockwiso current is induced
C. Clockwise current is induced
D. Only e.m.f. is induced

Answer

To solve the problem step by step, we will analyze the situation involving the circular loop in a magnetic field and the induced current when the loop is stretched.

### Step 1: Understand the Setup
We have a circular loop made of a flexible conducting material placed in a magnetic field that is directed perpendicularly into the plane of the loop.

**Hint:** Visualize the loop and the magnetic field direction. The magnetic field lines are entering the plane of the loop.

### Step 2: Analyze the Action
The loop is held at diametrically opposite points and is suddenly stretched outwards. This stretching changes the shape and area of the loop.

**Hint:** Consider how stretching the loop affects its area. The area of the loop will increase as it is stretched.

### Step 3: Determine the Change in Magnetic Flux
The magnetic flux (Φ) through the loop is given by the formula:
\[ \Phi = B \cdot A \]
where \(B\) is the magnetic field strength and \(A\) is the area of the loop. As the loop is stretched, the area \(A\) increases, leading to a change in magnetic flux.

**Hint:** Remember that the magnetic field \(B\) is constant, so the change in flux is primarily due to the change in area.

### Step 4: Calculate the Induced EMF
According to Faraday's law of electromagnetic induction, the induced EMF (ε) in the loop is given by:
\[ \epsilon = -\frac{d\Phi}{dt} \]
Since the area is increasing, \(dA/dt\) is positive, which means that \(d\Phi/dt\) is also positive.

**Hint:** The negative sign indicates the direction of the induced EMF opposes the change in flux.

### Step 5: Determine the Direction of Induced Current
Using Lenz's law, the induced current will flow in a direction that opposes the change in magnetic flux. Since the area is increasing, the magnetic flux through the loop is increasing. Therefore, the induced current will flow in a direction that tries to decrease the magnetic flux.

**Hint:** Apply the right-hand rule to determine the direction of the induced current. If the magnetic field is into the page, the induced current will flow in a clockwise direction to oppose the increase in flux.

### Step 6: Conclusion
The induced current in the loop, when it is stretched, will be in a clockwise direction.

**Final Answer:** The induced current will be clockwise.