| Directions: In the following questions, a statement of Assertion [A] is followed by a statement of Reason (R). Mark the correct choice as: |
| Assertion [A]: The magnetic field at the ends of a very long current carrying solenoid is half of that at the centre. |
| Reason (R): If the solenoid is sufficiently long, the field within it is uniform. |
A) Both Assertion [A] and Reason (R) are true and Reason (R) is the correct explanation of Assertion [A]
B) Both Assertion [A] and Reason (R) are true but Reason (R) is not the correct explanation of Assertion [A]
C) Assertion [A] is true but Reason (R) is false
D) Assertion [A] is false and Reason (R) is also false
Correct Answer: B
Solution :
[b] The magnetic field of a solenoid is given by, \[B=\frac{1}{2}{{\mu }_{0}}nl[cos\,{{\theta }_{1}}-cos{{\theta }_{2}}]\] For a very long current carrying solenoid, the magnetic field at the ends of a very long solenoid is given by, \[B=\frac{1}{2}{{\mu }_{0}}nl=\frac{1}{2}\times \text{Magnetic}\,\,\text{field}\,\,\text{at}\,\,\text{the}\,\,\text{centre}\text{.}\] \[[\because \,{{\theta }_{1}}=90{}^\circ ,{{\theta }_{2}}=180{}^\circ ]\]
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