Read the given statements and mark the correct option. Statement 1: Magnetic field inside a current carrying solenoid is greater than that of outside. Statement 2: Magnetic field at the centre of a current carrying circular loop is always zero.
A
Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B
Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1.
C
Statement 1 is true but statement 2 is false.
D
Statement 1 is false but statement 2 is true.
Text Solution
AI Generated Solution
The correct Answer is:
To solve the question, we need to evaluate the two statements provided:
**Statement 1**: Magnetic field inside a current carrying solenoid is greater than that of outside.
**Statement 2**: Magnetic field at the centre of a current carrying circular loop is always zero.
### Step-by-Step Solution:
1. **Evaluate Statement 1**:
- A solenoid is a long coil of wire that generates a magnetic field when an electric current passes through it.
- The magnetic field inside a long solenoid is uniform and can be calculated using the formula:
\[
B_{\text{inside}} = \mu_0 \cdot n \cdot I
\]
where \( \mu_0 \) is the permeability of free space, \( n \) is the number of turns per unit length, and \( I \) is the current.
- Outside the solenoid, the magnetic field is negligible and can be considered as zero.
- Therefore, the magnetic field inside the solenoid is indeed greater than that outside.
**Conclusion**: Statement 1 is **True**.
2. **Evaluate Statement 2**:
- For a current-carrying circular loop, the magnetic field at the center is not zero.
- The magnetic field at the center of a circular loop can be calculated using the formula:
\[
B_{\text{center}} = \frac{\mu_0 \cdot I}{2R}
\]
where \( R \) is the radius of the loop.
- This shows that there is a magnetic field at the center of the loop, and it is proportional to the current flowing through the loop.
**Conclusion**: Statement 2 is **False**.
### Final Answer:
- Statement 1 is True.
- Statement 2 is False.
Thus, the correct option is that Statement 1 is true and Statement 2 is false.
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