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 of the circular loop being stretched in a magnetic field and determine the induced current based on electromagnetic induction principles.

### Step 1: Understand the Initial Setup
- A circular loop of conducting material is placed in a magnetic field that is directed perpendicularly into its plane.
- The magnetic field strength is denoted as \( B \).

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

### Step 2: Analyze the Action of Stretching the Loop
- The loop is held at diametrically opposite points and is suddenly stretched outwards.
- This stretching transforms the circular loop into an elliptical shape, which affects the area of the loop.

**Hint:** Consider how stretching the loop changes its shape and area. Recall that the area \( A \) of the loop is crucial for calculating magnetic flux.

### Step 3: Determine the Change in Magnetic Flux
- The magnetic flux \( \Phi \) through the loop is given by the formula:
\[ \Phi = B \times A \]
- As the loop is stretched, the area \( A \) decreases, leading to a decrease in magnetic flux \( \Phi \).

**Hint:** Remember that a change in area results in a change in magnetic flux. Think about how the area of an ellipse compares to that of a circle.

### Step 4: Apply Faraday's Law of Electromagnetic Induction
- According to Faraday's Law, a change in magnetic flux through a closed loop induces an electromotive force (EMF):
\[ \text{EMF} = -\frac{d\Phi}{dt} \]
- Since the magnetic flux is decreasing, the induced EMF will be positive, indicating that current will flow in the loop.

**Hint:** Recall that the negative sign in Faraday's Law indicates the direction of induced EMF opposes the change in flux.

### Step 5: Use Lenz's Law to Determine the Direction of Induced Current
- Lenz's Law states that the direction of induced current will be such that it opposes the change in magnetic flux.
- Since the magnetic flux is decreasing (due to the stretching of the loop), the induced current must create a magnetic field that opposes this decrease.

**Hint:** Think about the direction of the original magnetic field (into the plane). The induced current must create a magnetic field that also points into the plane.

### Step 6: Determine the Direction of Induced Current
- To create a magnetic field that points into the plane, the induced current must flow in a clockwise direction when viewed from above.

**Hint:** Use the right-hand rule: curl your fingers in the direction of the current, and your thumb will point in the direction of the magnetic field created by that current.

### Conclusion
- The induced current in the loop, as a result of stretching it in a magnetic field, is in the clockwise direction.

**Final Answer:** The correct option is that the induced current is clockwise.