There is a magnetic material of coercitivy `2xx10^(3)Am^(-1)`. What current should flow through solenoid of length 15 cm having 150 turns to demagnetise the substance completely?

Options

A. (a)`4A`
B. (b)`2.5A`
C. (c)`2A`
D. (d)`3.5A`

Answer

To solve the problem, we need to find the current that should flow through a solenoid to demagnetize a magnetic material with a given coercivity. Here are the steps to derive the solution:

### Step 1: Understand the Given Data
- Coercivity (H) = \(2 \times 10^3 \, \text{A/m}\)
- Length of the solenoid (L) = 15 cm = 0.15 m
- Number of turns (N) = 150

### Step 2: Calculate the Number of Turns per Unit Length
The number of turns per unit length (n) can be calculated using the formula:
\[ n = \frac{N}{L} \]
Substituting the values:
\[ n = \frac{150}{0.15} = 1000 \, \text{turns/m} = 10^3 \, \text{turns/m} \]

### Step 3: Use the Relationship Between Magnetic Field Intensity, Current, and Turns per Unit Length
The magnetic field intensity (H) in a solenoid is given by the formula:
\[ H = n \cdot I \]
Where:
- H = magnetic field intensity (A/m)
- n = number of turns per unit length (turns/m)
- I = current (A)

### Step 4: Rearrange the Formula to Solve for Current
We can rearrange the formula to find the current (I):
\[ I = \frac{H}{n} \]

### Step 5: Substitute the Known Values
Substituting the values of H and n:
\[ I = \frac{2 \times 10^3}{10^3} = 2 \, \text{A} \]

### Final Answer
The current that should flow through the solenoid to demagnetize the substance completely is:
\[ \boxed{2 \, \text{A}} \]