When the current through a solenoid increases at a constant rate, the induced current in the solenoid

Options

A. Is constant and is in the direction of the increasing current in it
B. Is a constant and is opposite to the direction of the increasing current in it.
C. Increases with time and is in the direction of increasing current in it.
D. Increases with time and is opposite to the direction of the increasing current in it

Answer

To solve the question regarding the behavior of induced current in a solenoid when the current through it increases at a constant rate, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- We have a solenoid through which the current is increasing at a constant rate. This means that the rate of change of current (di/dt) is constant.

2. **Applying Lenz's Law**:
- According to Lenz's Law, the direction of the induced current is such that it opposes the change in magnetic flux that produced it. The induced electromotive force (EMF) can be expressed as:
\[ \text{EMF} = -L \frac{di}{dt} \]
- Here, \(L\) is the inductance of the solenoid, and \(\frac{di}{dt}\) is the rate of change of current.

3. **Analyzing the Induced EMF**:
- Since the current is increasing at a constant rate, \(\frac{di}{dt}\) is a constant value. Therefore, the induced EMF will also be constant in magnitude.
- The negative sign indicates that the induced EMF (and hence the induced current) will flow in a direction that opposes the increase in current through the solenoid.

4. **Conclusion about Induced Current**:
- The induced current in the solenoid will be constant in magnitude and will flow in the opposite direction to the increasing current.

5. **Final Answer**:
- The induced current in the solenoid is constant and flows in the opposite direction to the increasing current.