A steady eletric current is flowing through a cylindrical wire :-
(a) the electric field at the axis of wire is zero
(b) the magnetic field at the axis of wire is zero
(c) the electric field in the vicinity of wire is Zero.
(d) the magnetic field in the vicinity of wire is Zero.

Options

A. a,b,c
B. b,c
C. only c
D. only b

Answer

To solve the problem, we need to analyze the behavior of electric and magnetic fields around a cylindrical wire carrying a steady electric current. Let's go through the statements one by one.

### Step-by-Step Solution:

1. **Understanding Electric Field at the Axis of the Wire:**
- When a steady electric current flows through a cylindrical wire, the net charge within any section of the wire does not change. This means that there is no accumulation of charge at the center (axis) of the wire.
- Therefore, the electric field at the axis of the wire is **zero**.
- **Conclusion:** Statement (a) is **true**.

2. **Understanding Magnetic Field at the Axis of the Wire:**
- According to Ampère's Law and the Biot-Savart Law, the magnetic field generated by a current-carrying wire is circular and concentric around the wire.
- At the very center (axis) of the wire, the contributions to the magnetic field from all the current elements cancel each other out.
- Therefore, the magnetic field at the axis of the wire is **zero**.
- **Conclusion:** Statement (b) is **true**.

3. **Understanding Electric Field in the Vicinity of the Wire:**
- In the vicinity of a current-carrying wire, the electric field is not zero. The electric field is present due to the potential difference that drives the current through the wire.
- Therefore, the electric field in the vicinity of the wire is **not zero**.
- **Conclusion:** Statement (c) is **false**.

4. **Understanding Magnetic Field in the Vicinity of the Wire:**
- In the vicinity of a current-carrying wire, a magnetic field is generated around the wire. The direction of the magnetic field can be determined using the right-hand rule.
- Therefore, the magnetic field in the vicinity of the wire is **not zero**.
- **Conclusion:** Statement (d) is **false**.

### Final Answer:
The correct statements are:
- (a) The electric field at the axis of the wire is zero. **(True)**
- (b) The magnetic field at the axis of the wire is zero. **(True)**
- (c) The electric field in the vicinity of the wire is zero. **(False)**
- (d) The magnetic field in the vicinity of the wire is zero. **(False)**

Thus, the correct options are (a) and (b).