MHT CET · Physics · Magnetic Effects of Current
A solenoid \(2 \mathrm{~m}\) long and \(4 \mathrm{~cm}\) in diameter has 4 layers of windings of 1000 turns each and carries a current of \(5 \mathrm{~A}\). what is the magnetic field at its centre along the axis?
\(\left[\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}\right]\)
- A \(10^{-3} \mathrm{~T}\)
- B \(2 \pi \times 10^{-3} \mathrm{~T}\)
- C \(4 \pi \times 10^{-3} \mathrm{~T}\)
- D \(8 \pi \times 10^{-3} \mathrm{~T}\)
Answer & Solution
Correct Answer
(C) \(4 \pi \times 10^{-3} \mathrm{~T}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{B}=\mu_0 \mathrm{nI} \\ & \mathrm{n}=\frac{\mathrm{N}}{\mathrm{L}}=\frac{4 \times 1000}{2}=2000 \text { turns } / \mathrm{m}, \mathrm{I}=5 \mathrm{~A} \\ & \therefore \mathrm{B}=4 \pi \times 10^{-7} \times 2000 \times 5 \\ & =4 \pi \times 10^{-3} \mathrm{~T}\end{aligned}\)
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