KCET · Physics · Magnetic Effects of Current
A long solenoid with \( 40 \) turns per cm carries a current of \( 1 \mathrm{~A} \). The magnetic energy stored per unit volume is \( J m^{-3} \).
- A \( 3.2 \pi \)
- B ○ \( 32 \) п
- C \( 1.6 \) п
- D \( 6.4 \pi \)
Answer & Solution
Correct Answer
(A) \( 3.2 \pi \)
Step-by-step Solution
Detailed explanation
Given, number of turns \( =40 \) turns per \( \mathrm{cm} \); current \( =1 \mathrm{~A} \)
Therefore, magnetic energy stored per unit volume \( =\frac{1}{2} \mu_{0} n^{2} I^{2} \)
\(=\frac{1}{2} \times\left(4 \Pi \times 10^{-7}\right) \times\left(40 \times 10^{2}\right)^{2} \times(1)^{2}\)
\(=\frac{4 \times 4 \times 4 \times_{\Pi} \times 10^{-7} \times 10^{5}}{2}\)
\(=32 \times \Pi \times 10^{-1}=3.2 \Pi\)
Thus, magnetic energy stored per unit volume \( =3.2 \mathrm{IJ} \mathrm{m}^{-3} \)
Therefore, magnetic energy stored per unit volume \( =\frac{1}{2} \mu_{0} n^{2} I^{2} \)
\(=\frac{1}{2} \times\left(4 \Pi \times 10^{-7}\right) \times\left(40 \times 10^{2}\right)^{2} \times(1)^{2}\)
\(=\frac{4 \times 4 \times 4 \times_{\Pi} \times 10^{-7} \times 10^{5}}{2}\)
\(=32 \times \Pi \times 10^{-1}=3.2 \Pi\)
Thus, magnetic energy stored per unit volume \( =3.2 \mathrm{IJ} \mathrm{m}^{-3} \)
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