A solenoid of 1000 turns is wound uniform on a glass tube of 50cm long and 10 cm in diameter. Find the strength of magnetic field at the centre of solenoid when 0.1 amp current is flowing through it

Options

A. 200 amp-turns/meter
B. 50 amp
C. 10 amp-turns/meter
D. 200 amp

Explanation

To find the strength of the magnetic field at the center of a solenoid, we can use the formula for the magnetic field inside a solenoid:

\[ B = \mu_0 \cdot n \cdot I \]

where:
- \( B \) is the magnetic field strength,
- \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \, \text{T m/A} \)),
- \( n \) is the number of turns per unit length of the solenoid,
- \( I \) is the current flowing through the solenoid.

### Step 1: Calculate the number of turns per unit length (n)

Given:
- Total number of turns \( N = 1000 \)
- Length of the solenoid \( L = 50 \, \text{cm} = 0.5 \, \text{m} \)

The number of turns per unit length \( n \) is given by:

\[ n = \frac{N}{L} = \frac{1000}{0.5} = 2000 \, \text{turns/m} \]

### Step 2: Substitute values into the magnetic field formula

Now we can substitute \( n \) and \( I \) into the magnetic field formula. Given that the current \( I = 0.1 \, \text{A} \):

\[ B = \mu_0 \cdot n \cdot I \]

Substituting the values:

\[ B = (4\pi \times 10^{-7}) \cdot (2000) \cdot (0.1) \]

### Step 3: Calculate B

Calculating the above expression:

\[ B = (4\pi \times 10^{-7}) \cdot (200) = 800\pi \times 10^{-7} \, \text{T} \]

Using \( \pi \approx 3.14 \):

\[ B \approx 800 \cdot 3.14 \times 10^{-7} = 2.512 \times 10^{-4} \, \text{T} = 0.0002512 \, \text{T} \]

### Step 4: Calculate the magnetic field strength (H)

The magnetic field strength \( H \) is given by:

\[ H = \frac{B}{\mu_0} \]

Substituting the values:

\[ H = \frac{2.512 \times 10^{-4}}{4\pi \times 10^{-7}} \]

Calculating \( H \):

\[ H = \frac{2.512 \times 10^{-4}}{1.2566 \times 10^{-6}} \approx 200 \, \text{A/m} \]

### Final Answer

Thus, the strength of the magnetic field at the center of the solenoid is:

\[ H \approx 200 \, \text{A/m} \]