AP EAMCET · PHYSICS · Magnetic Effects of Current
The magnetic field at the centre of a long solenoid having 400 turns per unit length and carrying a current ' \(i\) ' is \(6.24 \times 10^{-2} \mathrm{~T}\). The magnetic field at the centre of another long solenoid having 200 turns per unit length and carrying a current \(\frac{' i^{\prime}}{2}\) is
- A \(1.56 \times 10^{-2} \mathrm{~T}\)
- B \(2.4 \times 10^{-2} \mathrm{~T}\)
- C \(26 \times 10^{-2} \mathrm{~T}\)
- D \(2.6 \times 10^{-2} \mathrm{~T}\)
Answer & Solution
Correct Answer
(A) \(1.56 \times 10^{-2} \mathrm{~T}\)
Step-by-step Solution
Detailed explanation
\(B = \mu_0 n i\) \(B_1 = \mu_0 (400) i = 6.24 \times 10^{-2} \mathrm{~T}\) \(B_2 = \mu_0 (200) \left(\frac{i}{2}\right) = \mu_0 (100) i\) \(B_2 = \frac{100}{400} B_1 = \frac{1}{4} (6.24 \times 10^{-2} \mathrm{~T})\) \(B_2 = 1.56 \times 10^{-2} \mathrm{~T}\)
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