A bar magnet is dropped into a vertical copper tube, considering the air resistance as negligible , the magnet acquired a constant speed . If the tube is heated the terminal velocity will be :-

Options

A. Decrease
B. Increase
C. Remain unchanged
D. Datas are incomplete

Answer

To solve the problem of what happens to the terminal velocity of a bar magnet dropped into a vertical copper tube when the tube is heated, we can follow these steps:

### Step 1: Understanding Terminal Velocity
When the bar magnet is dropped into the copper tube, it initially accelerates due to gravity. However, as it falls, it induces an electromotive force (emf) in the copper tube due to electromagnetic induction (Faraday's Law). This induced emf generates eddy currents in the copper, which create a magnetic field opposing the motion of the magnet (Lenz's Law). Eventually, the magnet reaches a constant speed known as terminal velocity, where the downward gravitational force (mg) is balanced by the upward magnetic force due to the eddy currents.

### Step 2: Effect of Heating the Copper Tube
When the copper tube is heated, the resistance of the copper increases. According to Ohm's Law, the induced current (I) in the tube is given by:
\[ I = \frac{E_{\text{induced}}}{R} \]
where \( E_{\text{induced}} \) is the induced emf and \( R \) is the resistance of the copper tube. As the resistance increases due to heating, the current induced in the copper tube decreases.

### Step 3: Impact on Eddy Currents and Magnetic Field
With a decrease in the induced current, the strength of the magnetic field generated by the eddy currents also decreases. Since the opposing magnetic force that acts against the falling magnet is directly related to the strength of the induced current and the resulting magnetic field, a decrease in the magnetic field means that the opposing force will also decrease.

### Step 4: Resulting Change in Terminal Velocity
Since the gravitational force (mg) remains constant and the opposing magnetic force decreases due to the reduced current and magnetic field, the balance of forces is disrupted. Consequently, the magnet will fall faster until a new terminal velocity is reached. This new terminal velocity will be higher than the original terminal velocity because the opposing force is weaker.

### Conclusion
Thus, when the copper tube is heated, the terminal velocity of the bar magnet will **increase**.