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 _______

A current of $45 \mathrm{A}$ is passing through an infinitely long wire which lies along the axis of an infinitely long solenoid of radius $1 \mathrm{cm}$. The magnetic field produced by the solenoid in the direction of the current in the wire is $4\mathrm{mT}$. What is the approximate magnitude of the resultant magnetic field at a point $3 \mathrm{mm}$ radially away from the solenoid acis? (Use ${\mu }_0=4\pi \times {10}^{-7} \mathrm{T} \mathrm{m}/\mathrm{A}$ )

The magnetic field inside a long solenoid 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.

The mean radius of a toroid is $10 \mathrm{cm}$ and a number of turns are $500$. If the current flowing through it is $0.1$ $\mathrm{A}$. Then, the value of magnetic field (in Tesla) for toroid:-

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 straight solenoid of length $50 \mathrm{cm}$, having $100$ turns carries a current of $2.5 \mathrm{A}$. The magnetic field at one end of the solenoid is $\dots \dots \times {10}^{-4} \mathrm{T}$

A long solenoid has $100$ turns/meter and a current of $3.5 \mathrm{A}$ is flowing through it. If it is filled with material of relative permeability $\left({\mu }_{\mathrm{r}}=20\right)$ then
magnetic field within the solenoid will be?

Ratio of magnetic field produced at centre & end points of long solenoid is

The centres of the turns of a toroid form a circle with a radius of $14.0\mathrm{ }\mathrm{cm}$. The cross-sectional area of each turn is $3.00 {\mathrm{cm}}^2$. It is wound with $5278$ turns of fine wire, and the wire carries a current of $4.00\mathrm{ }\mathrm{A}$. The core is filled with a paramagnetic material of magnetic susceptibility $2.90\times {10}^{-4}$. What would be the magnitude of the magnetic field within the substance?

A constant current i is maintained in a solenoid. Which of the following quantities will not increase if an iron rod is inserted in the solenoid along its axis ?

A toroidal solenoid is given which has inner and outer radii as $28 \mathrm{cm}$ and $29 \mathrm{cm}$ respectively. If it is constructed with $3700$ turns of wire around the core and a current of $10 \mathrm{A}$ flows in it, then calculate the magnetic field inside the core of the toroid.

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 $2.5 \mathrm{A}$.

Consider a closely wound solenoid of the cross-sectional area, $2\times {10}^{-4} {\mathrm{m}}^2$ having $3000$ turns. If this solenoid is carrying a current of $6 \mathrm{A}$ and suspended through its centre such that it can turn in a horizontal plane, then find the magnetic moment associated with this solenoid.

Find the magnitude of the magnetic field inside a solenoid of length $0.6 \mathrm{m}$ and has a radius of $2 \mathrm{cm}$. Assume that the solenoid is made up of $600$ turns and carries $4 \mathrm{A}$ of current.

What is the magnetisation of a solenoid with $1000$ turns per meter having a core of material whose relative permeability is $500$ and the winding of the solenoid is insulated from the core and carries a current of $2\mathrm{A}$?