Magnetic Field on the Axis of a Circular Current Loop

Two concentric coils $X$ and $Y$ of radii $16 \mathrm{cm}$ and $10 \mathrm{cm}$ lie in the same vertical plane containing $N-S$ direction. $X$ has $20$ turns and carries $16 \mathrm{A}$. $Y$ has $25$ turns & carries $18 \mathrm{A}$. $X$ has current in anticlockwise direction. The magnitude of net magnetic field at their common centre is-

Three rings, each having equal radius R, are placed mutually perpendicular to each other and each having its centre at the origin of co-ordinate system. If current I is flowing through each ring then the magnitude of the magnetic field at the common centre is

Find the magnetic induction at the origin in the figure shown.

Two circular coils A and B of radius $\frac{5}{\sqrt{2}}$ cm and 5 cm respectively current 5 Amp. and $\frac{5}{\sqrt{2}}$ Amp. respectively. The plane of B is perpendicular to plane of A their centres coincide. Find the magnetic field at the centre.

Find out the expression for the magnetic field at a point on the centre of a coil of radius carrying current I and having N number of turns.

Two identical current carrying coils with same centre are placed with their planes perpendicular to each other as shown. If $i= \sqrt{2} \mathrm{A}$ and radius of coil is $R= 1 \mathrm{m}$, then magnetic field at centre $C$ is equal to

A current carrying wire AB of the length $2\mathrm{\pi R}$ along a circle, as shown in figure. The magnetic field at the centre O is

Find out the magnetic field at axial point 'P' of solenoid shown in figure (where turn density $\text{'}n\text{'}$ and current through it is $I$)

The magnetic induction at the centre O is

A circular coil of wire of radius $r$ has $n$ turns and carries a current $I$. The magnetic induction $B$ at a point on the axis of the coil at a distance $\sqrt{3}r$ from its centre is

A wire carrying the current of $5 \mathrm{A}$ and length of $20 \mathrm{cm}$ is bent to form a semi-circle. The magnetic induction (in tesla) at centre of semi-circle is [use $\pi =\sqrt{10}$]

The strength of earth's magnetic field at a point is $0.4\times {10}^{-5} \mathrm{T}$. If this field is to be annulled by the magnetic induction produced at the centre of a circular conducting loop of radius $\pi \mathrm{cm}$, the current to be sent through the loop is

Considering magnetic field along the axis of a circular loop of radius $1$ meter, at what distance from the centre of the loop the magnetic field is $\frac{1}{2\sqrt{2}}$ times of its value at the centre?

A circular coil of radius $10 \mathrm{cm}$, carries a current of $40$ ampere. If it has $40$ turns, the flux density at the centre of the coil is (in $\mathrm{Wb} {\mathrm{m}}^{-2}$)

The radius of a circular current carrying coil is $R$. At what distance from the centre of the coil on its axis, the intensity of magnetic field will be $\frac{1}{2\sqrt{2}}$ times that at the centre$?$

Two circular loop of radii $10\mathrm{cm}$ and $40\mathrm{cm}$ carries current of $1 \mathrm{A}$ and $2 \mathrm{A}$ respectively. Find the ratio of magnitude of magnetic field at their centres

Consider a circular current-carrying coil $1$ of radius $R$ and magnetic moment $m=1 \mathrm{A}{ \mathrm{m}}^2$. The magnetic field due to coil $1$ at point $P$ in the plane of the coil $r\left(r\gg R\right)$ distance away from the center of the coil is $4\times {10}^{-4} \mathrm{Wb} {\mathrm{m}}^{-2}$. Consider another circular current-carrying coil $2$ of radius $R$ and magnetic moment $m^{\text{'}}$. The magnetic field due to coil $2$ at point $Q$ along the axis of the coil $r$ distance away from the center of the coil is ${10}^{-3} \mathrm{Wb} {\mathrm{m}}^{-2}$. When coil $2$ is placed in a uniform magnetic field of ${10}^{-4} \mathrm{T}$ in such a way that the plane of the coil is parallel to the magnetic field, find the torque experienced by the coil.

A point charge of $0.1 \mathrm{C}$ is placed on the circumference of a non-conducting ring of radius $1 \mathrm{m}$ which is rotating with a constant angular acceleration of $1 \mathrm{rad} {\mathrm{s}}^{-2}$. If ring starts it's motion at $t=0 \mathrm{s}$, the magnetic field at the centre of the ring at $t=10\sec$, is

Two wires A and B have lengths $40 \mathrm{cm}$ and $30 \mathrm{cm}$ respectively. A is bent as a circle of radius $r$ and B into an arc of radius $r$. A current $i_1$ is passed through A and $i_2$ through B. To have same magnetic field at the centre, the ratio of $i_1$: $i_2$ is

Two circular coils, each having $1000$turns and radius $R=0.25 \mathrm{m}$, are placed co-axially. Each coil is separated by a distance $1.0 \mathrm{m}$ from the point $P$ as shown in the figure. The coils carry equal currents $2.0 \mathrm{A}$ in the same direction. An identical configuration of coils is placed perpendicular to the previous arrangement as shown in the figure. The magnitude of magnetic field at point $P$ is closest to