Solenoids of variable lengths (l) and number of turns (N) but of equal radius carry a current of 5 A. Arrange the magnitudes of magnetic fields in them in ascending order.
(A) l = 0.5 m, N = 500
(B) l = 1.0 m, N = 500
(C) l = 0.5 m, N = 1000
(D) l = 1.5 m, N = 1000
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B), (D), (A), (C)
The field inside a long solenoid depends only on the number of turns per unit length and the current, not on the radius. With the same current, the field is proportional to \( n = N/l \).
\( \displaystyle B = \mu_0 n I = \mu_0 \frac{N}{l} I \)
\( \displaystyle (A)\ l = 0.5\,\mathrm{m},\ N = 500:\ n = \frac{500}{0.5\,\mathrm{m}} = 1000\,\mathrm{m^{-1}} \)
\( \displaystyle (B)\ l = 1.0\,\mathrm{m},\ N = 500:\ n = \frac{500}{1.0\,\mathrm{m}} = 500\,\mathrm{m^{-1}} \)
\( \displaystyle (C)\ l = 0.5\,\mathrm{m},\ N = 1000:\ n = \frac{1000}{0.5\,\mathrm{m}} = 2000\,\mathrm{m^{-1}} \)
\( \displaystyle (D)\ l = 1.5\,\mathrm{m},\ N = 1000:\ n = \frac{1000}{1.5\,\mathrm{m}} \approx 667\,\mathrm{m^{-1}} \)
Ascending order of n, and so of B: (B), (D), (A), (C).