KCET · Physics · Magnetic Effects of Current
A solenoid is 1 m long and 4 cm in diameter. It has five layers of windings of 1000 turns each and carries a current of 7 A . The magnetic field at the centre of the solenoid is
- A \(0.4396 \times 10^{-5} \mathrm{~T}\)
- B \(4.396 \times 10^{-2} \mathrm{~T}\)
- C \(43.96 \times 10^{-2} \mathrm{~T}\)
- D 439.6 T
Answer & Solution
Correct Answer
(B) \(4.396 \times 10^{-2} \mathrm{~T}\)
Step-by-step Solution
Detailed explanation
\(\ell=1 \mathrm{~m} ; \mathrm{r}=2 \mathrm{~cm} ; \mathrm{N}=5000 ; \mathrm{t}=7 \mathrm{~A} ; \sin \theta \approx 1\)
\(\mathrm{B}=\frac{\mu_0 \mathrm{Ni}}{\ell} \sin \theta\)
\(\begin{aligned} & B=\frac{4 \pi \times 10^{-7} \times 5000 \times 7 \times 1}{1} \\ & B=4.396 \times 10^{-2} \mathrm{~T}\end{aligned}\)
\(\mathrm{B}=\frac{\mu_0 \mathrm{Ni}}{\ell} \sin \theta\)
\(\begin{aligned} & B=\frac{4 \pi \times 10^{-7} \times 5000 \times 7 \times 1}{1} \\ & B=4.396 \times 10^{-2} \mathrm{~T}\end{aligned}\)
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