TS EAMCET · Physics · Magnetic Effects of Current
Two identical wires, carrying equal currents are bent into circular coils \(A\) and \(B\) with 2 and 3 turns respectively. The ratio of the magnetic fields at the centres of the coils \(A\) and B is
- A \(4: 9\)
- B \(2: 3\)
- C \(9: 4\)
- D \(3: 2\)
Answer & Solution
Correct Answer
(A) \(4: 9\)
Step-by-step Solution
Detailed explanation
\(N_A r_A = N_B r_B \implies 2r_A = 3r_B \implies r_A = \frac{3}{2}r_B\) \(\frac{B_A}{B_B} = \frac{(\mu_0 N_A I)/(2r_A)}{(\mu_0 N_B I)/(2r_B)} = \frac{N_A r_B}{N_B r_A}\) \(\frac{B_A}{B_B} = \frac{2 \cdot r_B}{3 \cdot (\frac{3}{2}r_B)} = \frac{2}{9/2} = \frac{4}{9}\)
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