| ASSERTION: The magnetic field at the ends of a very long current carrying solenoid is half of that at the center. |
| REASON: If the solenoid is sufficiently long, the field within it is uniform. |
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true and reason is not the correct explanation of assertion.
C) If assertion is true but reason is false.
D) If both assertion and reason are false.
E) If assertion is false but reason is true.
Correct Answer: B
Solution :
The magnetic field of a solenoid is given by \[B=\frac{1}{2}{{\mu }_{0}}n\,I\left[ \cos {{\theta }_{1}}-\cos {{\theta }_{2}} \right]\] For a very long current carrying solenoid, the magnetic field at the ends of a very long solenoid is given by, \[{{\theta }_{1}}=90{}^\circ \], \[{{\theta }_{2}}=180{}^\circ \] i.e. \[BV=\frac{1}{2}{{\mu }_{0}}nI=\frac{1}{2}\times \]Magnetic field at the center.
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