A coil carrying electric current is placed in uniform magnetic field

Options

A. torque is formed
B. emf is induced
C. Both (a) and (b) are correct
D. None of the above

Answer

To solve the problem of whether a coil carrying electric current placed in a uniform magnetic field experiences torque, EMF, or both, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
We have a coil that carries an electric current and is placed in a uniform magnetic field. We need to analyze the forces acting on the coil and determine if torque or EMF is induced.

**Hint**: Visualize the coil and the magnetic field direction. Draw a diagram to help you understand the orientation.

2. **Identify the Forces on the Coil**:
The force on a current-carrying conductor in a magnetic field is given by the equation:
\[ F = I \cdot L \times B \]
where \( I \) is the current, \( L \) is the length of the conductor, and \( B \) is the magnetic field.

**Hint**: Remember that the direction of the force can be determined using the right-hand rule.

3. **Analyze Each Segment of the Coil**:
For segments of the coil parallel to the magnetic field (let's say segments P and Q), the angle \( \theta \) between the current direction and magnetic field is 0 or 180 degrees. Therefore, the force on these segments will be zero:
\[ F = 0 \quad (\text{for segments P and Q}) \]

**Hint**: Check the angles between the current direction and the magnetic field for each segment.

4. **Calculate Forces on Other Segments**:
For the segments perpendicular to the magnetic field (let's say segments R and S), the angle \( \theta \) is 90 degrees, resulting in maximum force:
\[ F = I \cdot L \cdot B \quad (\text{for segments R and S}) \]
The forces will act in opposite directions on these segments.

**Hint**: Use the right-hand rule to find the direction of the forces on these segments.

5. **Determine the Torque**:
The forces acting on segments R and S will create a torque about the axis of the coil. The torque \( \tau \) can be calculated as:
\[ \tau = r \cdot F \]
where \( r \) is the distance from the axis to the line of action of the force.

**Hint**: Visualize how the forces will cause the coil to rotate about its axis.

6. **Check for Induced EMF**:
The induced EMF in a coil can be calculated using:
\[ \text{EMF} = -\frac{d\Phi}{dt} \]
where \( \Phi \) is the magnetic flux. In this case, since the area of the coil and the magnetic field are uniform and constant, there is no change in flux:
\[ \text{EMF} = 0 \]

**Hint**: Consider whether the area or magnetic field is changing over time.

7. **Conclusion**:
Since torque is present due to the forces on segments R and S, but no EMF is induced, the correct conclusion is that torque is formed, but EMF is not induced.

**Final Answer**: Torque is formed (Option A), and EMF is not induced.