Solenoid and Toroid

Using Ampere’s circuital law,obtain an expression for the magnetic field along the axis of a current carrying solenoid of length l and having N number of turns.

Field inside a solenoid is

A toroid of $n$ turns, mean radius $R$ and cross-sectional radius $a$ carries current $I.$ It is placed on a horizontal table taken as $xy$-plane. Its magnetic moment m _______

The magnetic field inside a long solenoid is

A long solenoid contains another coaxial solenoid whose radius $R$ is half of its own. Their coils have the same number of turns per unit length and initially both carry no current. At the same instant current start increasing linearly with time in both solenoid. At any moment the current flowing in the inner coil is twice as large as that in the outer one and their directions are the same. The ratio of the magnetic field at $r<R$ to $R<r<2 R$ is :

When the number of turns in a toroidal coil is doubled, then the value of magnetic flux density will become,

A short solenoid (length $l$ and radius $r$ with $n$ turns per unit length) lies well inside and on the axis of a very long, coaxial solenoid (length $L$, radius $R$ and $N$ turns per unit length, with $R>r$). Current $I$ follows in the short solenoid. Choose the correct statement.

An infinitely long solenoid of radius a $=\frac{5}{\pi }\mathrm{cm}$ and $10 \mathrm{turns} {\mathrm{cm}}^{-1}$ is placed such that its axis of symmetry lies along the $X$-axis. A current $I$ is flowing through the solenoid ( $X$ means that $I$ is flowing into and $·$ means it is flowing out of the page). A straight infinite wire with current $25 I$ is placed parallel to the $X-$axis at a distance $\frac{a}{2}$ away from the center. Which of the following gives the direction of net magnetic field at the origin?

A long solenoid has $200$ turns per cm and carries a current $i$. The magnetic field at its centre is $6.28\times {10}^{-2} \mathrm{Wb} {\mathrm{m}}^{-2}$. Another long solenoid has $100$ turns per $\mathrm{cm}$ and it carries a current $\frac{i}{3}.$ The value of the magnetic field at its centre is $\alpha \times {10}^{-2} \mathrm{Wb} {\mathrm{m}}^{-2}.$ Write the value of $\left[\alpha \right],$ where $\left[ \right]$ is the greatest integer function.

 Using Ampere’s circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis.

A cylindrical current carrying coil is called a _____.

A solenoid has length $0.5 \mathrm{m}$. Its winding is in double layer, each layer having $500$ turns. Its radius is $1.4 \mathrm{cm}$. Find magnetic field at its center when current in it is $5 \mathrm{A}$.

A $1.0 \mathrm{m}$ long solenoid has $100$ turns. Its radius is $1 \mathrm{cm}$. Find magnetic field at its axis, if current in it is $5 \mathrm{A}$. Find the force on electron moving with velocity ${10}^4 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$ along the axis.

Compare magnetic field of a bar magnet and a current-carrying solenoid. 

What is the difference between a current carrying solenoid and a bar magnet?

A long solenoid has six layers of windings of $450$ turns each. If diameter is $2.2 \mathrm{cm}$, length is $90 \mathrm{cm}$ and current carried is $6 \mathrm{A}$, then calculate the magnitude of magnetic field inside the solenoid.

Calculate the magnitude of magnetic induction at one end of a solenoid of $100$ turns and total length $50 \mathrm{cm}$ if it carries a current of $2.5 \mathrm{A}$.

Two current-carrying solenoids exhibit: 

Mark the polarity on the solenoid given below. What will happen if we insert a soft iron into it?

A tightly wound solenoid of radius $‘a’$ and length $‘l’$ has $n$ turns per unit length. It carries an electric current $i$. Magnetic field at a distance $\frac{l}{4}$ from one of the end (inside the solenoid on its axis) is $B=\frac{{\mu }_{0}ni\left(\sqrt{5}+3\right)}{\sqrt{K}}$ for $l=4a$ . Find the value of $K$.