Question

Assertion :The magnetic field at the ends of a very long current-carrying solenoid is half to that at the center. Reason: If the solenoid is sufficiently long, the field within it is uniform.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Both the statments are correct but the reason is not the correct explanation for Assertion.

As magnetic field at center of long solenoid, $B_c={\mu }_{o}nI$

Magnetic field at any point on the axis inside the solenoid, $B=\frac{{\mu }_{o}nI}{2}(cos{\theta }_1+cos{\theta }_2)$

Now for magnetic field at ends of long solenoid, ${\theta }_1=0$ and ${\theta }_2=90$

Thus, $B_e=\frac{{\mu }_{o}nI}{2}(1+0)=\frac{{\mu }_{o}nI}{2}$

Hence, $B_e=\frac{1}{2}{B}_c$