Question

To manufacture a solenoid of length ' \( l \) ' and inductance ' \( L \) ', the length of the thin wire required is (cross - sectional diameter of a solenoid is considerably less than length, \( \mu_0 = \) permeability of free space)

• A. \( \left[ \frac{4\pi l L}{\mu_0} \right]^{1/2} \)
• B. \( \left[ \frac{2\pi l L}{\mu_0} \right]^{1/2} \)
• C. \( \left[ \frac{8\pi l L^2}{\mu_0} \right]^{\frac{1}{2}} \)
• D. \( \left[ \frac{\pi l^2 L}{\mu_0} \right]^{\frac{1}{2}} \)

Hint:

For solenoids: - $L \propto N^2$ - Relate turns with wire length using circumference

Answer 1

The Correct Option is A