A coil of 100 turns, carrying a current of 5A, is placed in a magnetic field of 2T. The area of each turn is 0.01 m\(^2\). What is the magnetic moment of the coil?
Show Hint
- 0.5 Am\(^2\)
5 Am\(^2\)
- 2 Am\(^2\)
1 Am\(^2\)
The Correct Option is B
Solution and Explanation
Magnetic Moment of a Coil
We are given the following data:
- Number of turns, \( N = 100 \)
- Current, \( I = 5 \, \text{A} \)
- Magnetic field, \( B = 2 \, \text{T} \)
- Area of each turn, \( A = 0.01 \, \text{m}^2 \)
Step 1: Recall the formula for the magnetic moment of a coil:
The magnetic moment \( \mu \) of a coil is given by the formula:
\[ \mu = N \cdot I \cdot A \]
Where:
- \( \mu \) is the magnetic moment,
- \( N \) is the number of turns,
- \( I \) is the current,
- \( A \) is the area of each turn of the coil.
Step 2: Substitute the known values into the formula:
\[ \mu = 100 \cdot 5 \cdot 0.01 = 5 \, \text{A} \cdot \text{m}^2 \]
Conclusion:
The magnetic moment of the coil is \( 5 \, \text{A} \cdot \text{m}^2 \).
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