As shown in the figure, à magnet is moved with a fast speed towards a coil at rest. Due to this induced emf, induced current and induced charge in the coll is E, I and Q respectively. If the speed of the magnet is doubled, the incorrect statement is

Options

A. E increases
B. I increases
C. O remains same
D. Q increases

Answer

To solve the problem, we need to analyze the effects of moving a magnet towards a coil at rest and how the induced electromotive force (emf), current, and charge are affected when the speed of the magnet is doubled.

### Step-by-Step Solution:

1. **Understanding Induced EMF**:
- According to Faraday's law of electromagnetic induction, the induced emf (E) in a coil is directly proportional to the rate of change of magnetic flux (Φ) through the coil. Mathematically, this can be expressed as:
\[ E = -\frac{d\Phi}{dt} \]
- When the magnet is moved towards the coil, the magnetic flux through the coil changes, inducing an emf.

**Hint**: Recall Faraday's law and how it relates to the change in magnetic flux.

2. **Effect of Doubling the Speed**:
- If the speed of the magnet is doubled, the rate of change of magnetic flux (dΦ/dt) will also increase. This is because a faster movement of the magnet leads to a quicker change in the magnetic field experienced by the coil.
- Therefore, the induced emf (E) will increase.

**Hint**: Consider how the speed of the magnet affects the rate of change of magnetic flux.

3. **Induced Current**:
- The induced current (I) in the coil is related to the induced emf by Ohm's law:
\[ I = \frac{E}{R} \]
- Since the induced emf (E) increases when the speed of the magnet is doubled, the induced current (I) will also increase, assuming the resistance (R) of the coil remains constant.

**Hint**: Use Ohm's law to relate induced current to induced emf.

4. **Induced Charge**:
- The induced charge (Q) in the coil can be defined as the product of current and time:
\[ Q = I \cdot t \]
- However, the time (t) for which the magnet is moved towards the coil does not change just because the speed of the magnet is doubled. The total charge induced depends on the total current over the time the current flows, which remains constant for a given time interval.

**Hint**: Think about how charge is calculated and whether the time duration changes with speed.

5. **Conclusion**:
- From the above analysis, we can conclude:
- The induced emf (E) increases.
- The induced current (I) increases.
- The induced charge (Q) remains the same.
- Therefore, the incorrect statement is that the induced charge (Q) increases when the speed of the magnet is doubled.

### Final Answer:
The incorrect statement is that the induced charge (Q) increases.