There is one long straight conductor carrying current which is kept along the dimaeter of a circular loop without touching it.

Options

A. emf induced in the loop is zero if AC current is flowing through the straight conductor
B. emf induced in the loop is zero if current in the straight conductor increases.
C. emf induced in the loop is zero if current in the straight conductor decreases.
D. emf induced in the loop is zero constant current flows through the straight conductor .

Explanation

To solve the problem, we need to analyze the situation of a long straight conductor carrying current placed along the diameter of a circular loop. We will examine the implications of this configuration on the induced electromotive force (EMF) in the loop.

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have a circular loop and a straight conductor placed along its diameter.
- The conductor carries a current (let's denote it as I).

2. **Magnetic Field Due to the Straight Conductor**:
- According to Ampère's Law, a long straight conductor carrying current produces a magnetic field around it.
- The direction of the magnetic field can be determined using the right-hand rule. If the current flows in a certain direction, the magnetic field will circulate around the conductor.

3. **Analyzing the Magnetic Field in the Loop**:
- The magnetic field produced by the straight conductor will be different in the upper and lower halves of the circular loop.
- For the upper half of the loop, if the current is flowing from left to right, the magnetic field will be directed out of the plane (towards us).
- For the lower half of the loop, the magnetic field will be directed into the plane (away from us).

4. **Calculating the Magnetic Flux**:
- The magnetic flux (Φ) through the loop is given by the product of the magnetic field (B) and the area (A) it penetrates: \( Φ = B \cdot A \).
- Since the area of the upper half and lower half of the loop is equal, we can denote the magnetic flux in the upper half as \( Φ = φ \) and in the lower half as \( Φ = -φ \).
- Therefore, the net magnetic flux through the loop is:
\[ Φ_{net} = φ + (-φ) = 0 \]

5. **Induced EMF Calculation**:
- According to Faraday's law of electromagnetic induction, the induced EMF (ε) in a loop is given by the rate of change of magnetic flux through the loop:
\[ ε = -\frac{dΦ}{dt} \]
- Since the net magnetic flux \( Φ_{net} = 0 \), the rate of change of flux \( \frac{dΦ}{dt} \) will also be zero:
\[ ε = -\frac{d(0)}{dt} = 0 \]

6. **Conclusion**:
- Regardless of whether the current in the conductor is constant, increasing, or decreasing, the induced EMF in the loop remains zero.

### Final Answer:
The induced EMF in the loop is zero.