Four students individually construct tightly wound coils of radii and number of turns as per details given below:
| S.no | Students | Radius of coil | Number of turns |
| A | Student-1 | \( 4 \) cm | \( 16 \) |
| B | Student-2 | \( 3 \) cm | \( 18 \) |
| C | Student-3 | \( 6 \) cm | \( 30 \) |
| D | Student-4 | \( 4 \) cm | \( 12 \) |
Arrange the coils made by four students according to the magnitude of the magnetic fields at their centers in decreasing order, if the current through them is same.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → B, C, A, D
The field at the centre of a tightly wound circular coil of N turns and radius r is \( B = \mu_0NI/2r \). With the same current in every coil, \( B \propto N/r \), so it is enough to compare N/r.
\( \text{A: } N/r = 16/4 = 4 \)
\( \text{B: } N/r = 18/3 = 6 \)
\( \text{C: } N/r = 30/6 = 5 \)
\( \text{D: } N/r = 12/4 = 3 \)
Decreasing order of field: B (6) > C (5) > A (4) > D (3), i.e. B, C, A, D.