Initially plane of coil is parallel to the uniform magnetic field B. In time `Deltat` it makes to perpendicular to the magnetic field, then charge flows in `Deltat` depends on this time as -

Options

A. `propDeltat`
B. `prop(1)/(Deltat)`
C. `prop(Deltat)^0`
D. `prop(Deltat)^2`

Explanation

To solve the problem, we need to analyze the situation where a coil is rotating in a magnetic field and determine how the charge that flows through the coil depends on the time taken for this rotation.

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- The coil is initially parallel to the magnetic field \( B \). In this position, the magnetic flux through the coil is zero because the angle between the magnetic field and the normal to the coil is \( 0^\circ \).

2. **Change in Orientation**:
- The coil rotates from being parallel to the magnetic field to being perpendicular to it. When the coil is perpendicular to the magnetic field, the magnetic flux through the coil is at its maximum. The angle between the magnetic field and the normal to the coil is \( 90^\circ \).

3. **Magnetic Flux Calculation**:
- The magnetic flux \( \Phi \) through the coil is given by:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
where \( A \) is the area of the coil and \( \theta \) is the angle between the magnetic field and the normal to the coil.
- Initially, \( \Phi_{\text{initial}} = 0 \) (when parallel) and finally, \( \Phi_{\text{final}} = B \cdot A \) (when perpendicular).

4. **Change in Magnetic Flux**:
- The change in magnetic flux \( \Delta \Phi \) as the coil rotates from parallel to perpendicular is:
\[ \Delta \Phi = \Phi_{\text{final}} - \Phi_{\text{initial}} = B \cdot A - 0 = B \cdot A \]

5. **Induced EMF**:
- According to Faraday's law of electromagnetic induction, the induced EMF \( \mathcal{E} \) in the coil is given by the rate of change of magnetic flux:
\[ \mathcal{E} = -\frac{d\Phi}{dt} \]
- The average induced EMF during the time \( \Delta t \) is:
\[ \mathcal{E} = \frac{\Delta \Phi}{\Delta t} = \frac{B \cdot A}{\Delta t} \]

6. **Current Calculation**:
- The current \( I \) flowing through the coil can be expressed as:
\[ I = \frac{\mathcal{E}}{R} = \frac{B \cdot A}{R \cdot \Delta t} \]
- Here, \( R \) is the resistance of the coil.

7. **Charge Flow Calculation**:
- The total charge \( Q \) that flows through the coil during the time \( \Delta t \) is given by:
\[ Q = I \cdot \Delta t = \left(\frac{B \cdot A}{R \cdot \Delta t}\right) \cdot \Delta t = \frac{B \cdot A}{R} \]

8. **Conclusion**:
- From the above calculations, we see that the charge \( Q \) is independent of the time \( \Delta t \) taken for the rotation. Thus, we conclude that the charge depends only on the orientation of the coil and not on the time taken for the rotation.

### Final Answer:
The charge \( Q \) that flows in time \( \Delta t \) is independent of \( \Delta t \) and can be expressed as:
\[ Q \propto \Delta t^0 \]