The Solenoid and the 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.

A long metallic wire is cut into two equal pieces. Two circular coils are made of them. One with radius $R_1$, has one turn and the other with radius $R_2$ has two turns. They are connected in series to an electrical circuit. The ratio of magnetic induction at the centre of the wires is 

What is the formula for magnetic field for a long solenoid?

The current required to be passed through a solenoid of $15 \mathrm{cm}$ length and $60$ turns in order to demagnetise a bar magnet of magnetic intensity $2.4\times {10}^3 \mathrm{A} {\mathrm{m}}^{–1}$ is ________ $\mathrm{A}$.

The magnetic intensity at the centre of a long current carrying solenoid is found to be $1.6 \times {10}^3 \mathrm{A} {\mathrm{m}}^{-1}$. If the number of turns is $8$ per $\mathrm{cm}$, then the current flowing through the solenoid is $\_\_\_\_\_\_\mathrm{A}.$

A linear solenoid is made of a copper wire of diameter $0.4 \mathrm{mm}$. It has a length of $10 \mathrm{cm}$, diameter $1 \mathrm{cm}$ and $1000$ turns. If the two ends of the solenoid is connected to a battery of emf $2 \mathrm{V}$ and current is sent through it, determine the magnetic field produced at the mid-point on the axis of the solenoid. Resistivity of copper = $1.76\times {10}^{-8} \mathrm{\Omega } \mathrm{m}$

A circular coil of radius $5 \mathrm{cm}$ and having $100$ turns is made of an insulated copper wire of diameter $0.4 \mathrm{mm}$. If current is sent through it by connecting its two ends with a battery of emf $2 \mathrm{V}$, what will be the magnetic field produced at its centre? Resistivity of copper: = $1.76\times {10}^{-8} \mathrm{\Omega } \mathrm{m}$

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 _______

A coil wrapped around toroid has inner radius of $20 \mathrm{cm}$ and an outer radius of $25 \mathrm{cm}.$ If the wire wrapping makes $800$ turns and carries a current of $12 \mathrm{A}.$ The maximum and minimum values of the magnetic field with in the toroid are _______

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,

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 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. 

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 $2.5 \mathrm{A}$.