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The B-H curve for a ferromagnet is shown...

The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with `1000` turns/cm. The current that should be passed in the solenoid to demagnetise the ferromagnet completely is :

A

2 mA

B

`20 mu A`

C

`1 mA`

D

`40 mu A`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of determining the current required to demagnetize a ferromagnet placed inside a solenoid, we will follow these steps: ### Step 1: Identify the Coercivity from the B-H Curve From the B-H curve provided in the question, we need to find the coercivity (H_c) of the ferromagnet. The coercivity is the value of the magnetic field strength (H) at which the magnetization (B) becomes zero. According to the transcript, the coercivity is given as: \[ H_c = 100 \, \text{A/m} \] ### Step 2: Determine the Number of Turns per Meter The problem states that the solenoid has 1000 turns per centimeter. We need to convert this to turns per meter: \[ n = 1000 \, \text{turns/cm} = 1000 \times 100 \, \text{turns/m} = 100000 \, \text{turns/m} \] ### Step 3: Relate H to Current (I) in the Solenoid The relationship between the magnetic field strength (H), the number of turns per unit length (n), and the current (I) flowing through the solenoid is given by the formula: \[ H = n \cdot I \] Where: - \( H \) is the magnetic field strength (A/m), - \( n \) is the number of turns per meter (turns/m), - \( I \) is the current (A). ### Step 4: Rearrange the Formula to Find I We can rearrange the formula to solve for the current \( I \): \[ I = \frac{H}{n} \] ### Step 5: Substitute the Values Now we can substitute the values of \( H \) and \( n \) into the equation: \[ I = \frac{100 \, \text{A/m}}{100000 \, \text{turns/m}} \] ### Step 6: Calculate the Current Calculating the above expression gives: \[ I = \frac{100}{100000} = 0.001 \, \text{A} \] This can also be expressed in milliamperes: \[ I = 1 \, \text{mA} \] ### Final Answer The current that should be passed in the solenoid to demagnetize the ferromagnet completely is: \[ \boxed{1 \, \text{mA}} \] ---
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