A magnet is in form of a bar as shown in the figure. The line joining the center of the bar and the center of the coil (central axis) is perpendicular to the plane of the oil. Which of the following motions of the bar will not induce electric current in the coil?

Options

A. Translation motion back and forth

B. Translation motion up and down

C. The bar axis is at angle to the central axis and spins around it.

D. The bar spins around an axis in the paper plane.

Answer

To determine which motion of the bar magnet will not induce an electric current in the coil, we need to analyze the relationship between the motion of the magnet and the change in magnetic flux through the coil. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Induction
According to Faraday's law of electromagnetic induction, an electromotive force (EMF) is induced in a coil when there is a change in magnetic flux through the coil. Therefore, we need to identify if the motion of the bar magnet causes a change in the magnetic flux through the coil.

### Step 2: Analyze Each Motion of the Magnet
Let’s evaluate the four options provided:

1. **Translation Motion (Moving towards or away from the coil)**:
- When the magnet moves towards or away from the coil, the magnetic field lines that pass through the coil change. This results in a change in magnetic flux, thus inducing an EMF and current in the coil.
- **Conclusion**: Current is induced.

2. **Up and Down Motion**:
- If the magnet moves up and down while the coil is fixed, the magnetic field lines that pass through the coil will also change. As the magnet moves up, the number of magnetic field lines passing through the coil increases, and as it moves down, they decrease.
- **Conclusion**: Current is induced.

3. **Rotating the Magnet in the Plane**:
- If the magnet is rotated around an axis that is perpendicular to the plane of the coil, the orientation of the magnetic field lines relative to the coil changes. However, if the rotation does not change the number of magnetic field lines passing through the coil (for example, if the magnet is rotated in such a way that it remains at a constant distance from the coil), the magnetic flux through the coil will not change.
- **Conclusion**: No current is induced.

4. **Rotating about a Perpendicular Axis**:
- When the magnet rotates around a line that is perpendicular to the plane of the coil, the magnetic field lines passing through the coil will change, leading to a change in magnetic flux. Therefore, an EMF and current will be induced.
- **Conclusion**: Current is induced.

### Step 3: Identify the Correct Option
From the analysis above, the only motion that does not induce an electric current in the coil is the third option, where the magnet is rotated in such a way that it does not change the flux through the coil.

### Final Answer
The motion of the bar that will not induce electric current in the coil is **Option 3**.

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