Solenoid

A capacitor of capacitance $100 \mathrm{\mu F}$is connected to a battery of $20 \mathrm{V}$ for a long time and then disconnected from it. It is now connected across a long solenoid having $4000 \mathrm{turns} \mathrm{per} \mathrm{meter}$. It is found that the potential difference across the capacitor drops to $90\%$ of its maximum value in $2.0 \mathrm{s}$. Estimate the average magnetic field produced at the centre of the solenoid during this period.

A tightly-wound, long solenoid is kept with its axis parallel to a large metal sheet carrying a surface current. The surface current through the width $dl$ of the sheet is $Kdl$ and the number of turns per unit length of the solenoid is $n$. The magnetic field near the centre of the solenoid is found to be zero,

$\left(\mathrm{a}\right)$ Find the current in the solenoid. $\left(\mathrm{b}\right)$ If the solenoid is rotated to make its axis perpendicular to the metal sheet, what would be the magnitude of the magnetic field near its centre?

A tightly-wound, long solenoid has $n$ turns per unit length, a radius $r$ and carries a current $i$. A particle having charge $q$ and mass $m$ is projected from a point on the axis in a direction perpendicular to the axis. What can be the maximum speed for which the particle does not strike the solenoid?

A tightly-wound, long solenoid carries a current of $2.00 \mathrm{A}$. An electron is found to execute a uniform circular motion inside the solenoid with a frequency of $1.00\times {10}^8 \mathrm{rev} {\mathrm{s}}^{-1}$. Find the number of turns per metre in the solenoid.

A tightly-wound solenoid of radius $a$ and length $\mathcal{l}$ has $n$ turns per unit length. It carries an electric current $i$. Consider a length $dx$ off the solenoid at a distance $x$ from one end. This contains $ndx$ turns and may be approximated as a circular current $i\mathit{ }n\mathit{ }dx$.

(a) Write the magnetic field at the centre of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the centre of the solenoid.

(b) Verify that if $\mathcal{l}>>\mathrm{a}$, the field tends to $B={\mu }_{0}ni$ , the and if $a>>\mathcal{l}$, the field tends to $B=\frac{{\mu }_{0}nil}{2a}$. Interpret these results.

A copper wire having resistance $0.01 \mathrm{ohm}$ in each metre is used to wind a $400$ turn solenoid of radius $1.0 \mathrm{cm}$ and length $20 \mathrm{cm}$. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of $1.0\times {10}^{-2} \mathrm{T}$ near the centre of the solenoid.

A long solenoid is fabricated by closely winding a wire of radius $0.5 \mathrm{mm}$ over a cylindrical nonmagnetic frame so that the successive turns nearly touch each other. What would be the magnetic field $B$ at the centre of the solenoid if it carries a current of $5 \mathrm{A}$?

The magnetic field $B$ inside a long solenoid, carrying a current of $5.00 \mathrm{A}$, is $3.14\times {10}^{-2} \mathrm{T}$. Find the number of turns per unit length of the solenoid.

The magnetic field inside a tightly wound, long solenoid is $B={\mu }_{0}ni.$ It suggests that the field does not depend on the total length of the solenoid, and hence if we add more loops at the ends of a solenoid the field should not increase. Explain qualitatively why the extra-added loops do not have a considerable effect on the field inside the solenoid.