A wire of length 100 m is tightly wounded on a hollow tube of radius 5 mm and length 1m . A current of 1 A is flowing in the wire. Then magnetic field strength inside the tube will be : -

Options

A. 4 T
B. 4 mT
C. 40 mT
D. 40 T

Answer

To find the magnetic field strength inside a hollow tube wound with a wire, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the parameters given in the problem:**
- Length of the wire (L) = 100 m
- Radius of the tube (r) = 5 mm = 5 x 10^-3 m
- Length of the tube (h) = 1 m
- Current (I) = 1 A

2. **Calculate the length of one turn of the wire:**
The length of one complete turn around the tube is given by the circumference of the tube:
\[ \text{Length of one turn} = 2\pi r = 2\pi(5 \times 10^{-3}) \text{ m} \]

3. **Calculate the total number of turns (N):**
The total number of turns is the total length of the wire divided by the length of one turn:
\[ N = \frac{L}{\text{Length of one turn}} = \frac{100}{2\pi(5 \times 10^{-3})} \]

4. **Calculate the number of turns per unit length (n):**
The number of turns per unit length is given by:
\[ n = \frac{N}{h} = \frac{N}{1} = N \]

5. **Substitute N into the formula for magnetic field strength (B):**
The magnetic field inside a solenoid is given by:
\[ B = \mu_0 n I \]
where \(\mu_0\) (permeability of free space) = \(4\pi \times 10^{-7} \text{ T m/A}\).

6. **Substituting the values:**
Substitute \(n\) and \(I\) into the equation:
\[ B = \mu_0 \left(\frac{100}{2\pi(5 \times 10^{-3})}\right) (1) \]

7. **Simplify the expression:**
- Calculate \(n\):
\[ N = \frac{100}{2\pi(5 \times 10^{-3})} = \frac{100}{0.0314} \approx 3183.1 \text{ turns} \]
- Therefore, \(n \approx 3183.1 \text{ turns/m}\).
- Now substitute \(n\) into the magnetic field formula:
\[ B = (4\pi \times 10^{-7}) (3183.1) (1) \]

8. **Final calculation:**
\[ B \approx 4\pi \times 10^{-7} \times 3183.1 \approx 4 \times 10^{-3} \text{ T} = 4 \text{ mT} \]

### Final Answer:
The magnetic field strength inside the tube will be approximately **4 mT (milliTesla)**.