358568
When current in a coil changes from \(5\;\,A\) to \(2\;\,A\) in \(0.1\;\,s\), an average voltage of \(50\,\;V\) is produced. The self inductance of the coil is :
358569
The length of a wire required to manufacture a solenoid of length \(l\) and self-induction \(L\) is (crosssectional area is negligible)
1 \(\sqrt{\dfrac{2 \pi L l}{\mu_{0}}}\)
2 \(\sqrt{\dfrac{\mu_{0} L l}{4 \pi}}\)
3 \(\sqrt{\dfrac{4 \pi L l}{\mu_{0}}}\)
4 \(\sqrt{\dfrac{\mu_{0} L l}{2 \pi}}\)
Explanation:
\(L=\dfrac{\mu_{0} N^{2} A}{l}\) If \(x\) is the length of the wire to manufacture the solenoid with \(\mathrm{r}\) as radius, then \(\quad x=2 \pi r N, A=\pi r^{2}\) \(\therefore L=\mu_{0}\left(\dfrac{x^{2}}{4 \pi^{2} r^{2}}\right) \dfrac{\pi r^{2}}{l} \Rightarrow x=\sqrt{\dfrac{4 \pi L l}{\mu_{0}}}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358570
A solenoid of length \(l\) with \(n\) turns per unit length has self inductance \(L\). If both \(n\) and \(l\) are doubled the self inductance will be
358568
When current in a coil changes from \(5\;\,A\) to \(2\;\,A\) in \(0.1\;\,s\), an average voltage of \(50\,\;V\) is produced. The self inductance of the coil is :
358569
The length of a wire required to manufacture a solenoid of length \(l\) and self-induction \(L\) is (crosssectional area is negligible)
1 \(\sqrt{\dfrac{2 \pi L l}{\mu_{0}}}\)
2 \(\sqrt{\dfrac{\mu_{0} L l}{4 \pi}}\)
3 \(\sqrt{\dfrac{4 \pi L l}{\mu_{0}}}\)
4 \(\sqrt{\dfrac{\mu_{0} L l}{2 \pi}}\)
Explanation:
\(L=\dfrac{\mu_{0} N^{2} A}{l}\) If \(x\) is the length of the wire to manufacture the solenoid with \(\mathrm{r}\) as radius, then \(\quad x=2 \pi r N, A=\pi r^{2}\) \(\therefore L=\mu_{0}\left(\dfrac{x^{2}}{4 \pi^{2} r^{2}}\right) \dfrac{\pi r^{2}}{l} \Rightarrow x=\sqrt{\dfrac{4 \pi L l}{\mu_{0}}}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358570
A solenoid of length \(l\) with \(n\) turns per unit length has self inductance \(L\). If both \(n\) and \(l\) are doubled the self inductance will be
358568
When current in a coil changes from \(5\;\,A\) to \(2\;\,A\) in \(0.1\;\,s\), an average voltage of \(50\,\;V\) is produced. The self inductance of the coil is :
358569
The length of a wire required to manufacture a solenoid of length \(l\) and self-induction \(L\) is (crosssectional area is negligible)
1 \(\sqrt{\dfrac{2 \pi L l}{\mu_{0}}}\)
2 \(\sqrt{\dfrac{\mu_{0} L l}{4 \pi}}\)
3 \(\sqrt{\dfrac{4 \pi L l}{\mu_{0}}}\)
4 \(\sqrt{\dfrac{\mu_{0} L l}{2 \pi}}\)
Explanation:
\(L=\dfrac{\mu_{0} N^{2} A}{l}\) If \(x\) is the length of the wire to manufacture the solenoid with \(\mathrm{r}\) as radius, then \(\quad x=2 \pi r N, A=\pi r^{2}\) \(\therefore L=\mu_{0}\left(\dfrac{x^{2}}{4 \pi^{2} r^{2}}\right) \dfrac{\pi r^{2}}{l} \Rightarrow x=\sqrt{\dfrac{4 \pi L l}{\mu_{0}}}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358570
A solenoid of length \(l\) with \(n\) turns per unit length has self inductance \(L\). If both \(n\) and \(l\) are doubled the self inductance will be
358568
When current in a coil changes from \(5\;\,A\) to \(2\;\,A\) in \(0.1\;\,s\), an average voltage of \(50\,\;V\) is produced. The self inductance of the coil is :
358569
The length of a wire required to manufacture a solenoid of length \(l\) and self-induction \(L\) is (crosssectional area is negligible)
1 \(\sqrt{\dfrac{2 \pi L l}{\mu_{0}}}\)
2 \(\sqrt{\dfrac{\mu_{0} L l}{4 \pi}}\)
3 \(\sqrt{\dfrac{4 \pi L l}{\mu_{0}}}\)
4 \(\sqrt{\dfrac{\mu_{0} L l}{2 \pi}}\)
Explanation:
\(L=\dfrac{\mu_{0} N^{2} A}{l}\) If \(x\) is the length of the wire to manufacture the solenoid with \(\mathrm{r}\) as radius, then \(\quad x=2 \pi r N, A=\pi r^{2}\) \(\therefore L=\mu_{0}\left(\dfrac{x^{2}}{4 \pi^{2} r^{2}}\right) \dfrac{\pi r^{2}}{l} \Rightarrow x=\sqrt{\dfrac{4 \pi L l}{\mu_{0}}}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358570
A solenoid of length \(l\) with \(n\) turns per unit length has self inductance \(L\). If both \(n\) and \(l\) are doubled the self inductance will be