Biot-Savart Law & Circular Coils

A circular coil having n turns, each of radius 'r' carries a current I. The magnetic field at a distance $x = \sqrt{8}\, r$ from its centre along the axis of the coil is ($\mu_0$ = permeability of free space)

The magnitude of magnetic induction at a point on the axis at a large distance $r$ from a centre of a circular coil of $n$ turns and area $A$ carrying current $i$ is ($\mu_0$ = permeability of free space)

A circular loop of radius R is carrying current I. The ratio of magnetic field at the center of circular loop and at a distance R from the center of the loop on its axis is

The magnetic field at the centre of a current carrying circular loop of radius $R$ is $16\ \mu\text{T}$. The magnetic field at a distance $x = \sqrt{3} R$ on its axis from the centre is

$\underline{\qquad}\ \mu\text{T}$.

An arc of a circle of radius R subtends an angle $\pi/2$ at the centre. It carries a current I. The magnetic field at the centre will be ($\mu_0$ = permeability of free space)

A circular arc of wire of radius of curvature $r$ subtends an angle of $\frac{\pi}{5}$ radian at its centre. If current $i$ is flowing in it then the magnetic induction at its centre is ($\mu_0$ = permeability of free space)

Two circular coils A and B are made from same wire but the radius of coil A is twice that of coil B. If the magnetic field at their centres is same then the ratio potential difference applied across them is

Two circular coils $A$ and $B$ are made from the same wire but the radius of coil $A$ is twice that of coil $B$. What is the ratio of potential difference applied across them, so that the magnetic field at their centres is the same?

The magnetic field at the center of circular coil carrying current '$I$' for a single turn of a given length of wire is '$B$'. The same wire is bent in a circular coil having two turns. When the same current passes through it, the value of magnetic field becomes

A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having n turns. If the same current is passed in both the cases, the ratio of magnetic field produced at the centre for one turn to that of n turns is

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $\alpha \times 10^{-14}\text{ J}$. The value of $\alpha$ is $\underline{\qquad}\ .\ \left(\mu_0 = 4\pi \times 10^{-7}\text{ Tm/A}, \pi = 3.14\right)$

A particle carrying a charge equal to $100$ times the charge of an electron is rotating one rotation per second in a circular path of radius $0.8$ m. The value of magnetic field produced at the centre will be ($\mu_0$ = permeability of free space)

A thin ring of radius 'R' metre has charge 'q' coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of 'f' revolution/s. The value of magnetic induction at the centre of the ring in Wb/m${}^{2}$ is

( $\mu_0$ = permeability of free space)

Consider a circular loop (radius $R$) carrying current $I$, the magnetic field produced by it at a point on the axis at a distance $z$ from the centre of the loop is $\frac{xR^2}{(z^2+R^2)^{3/2}}$. The value of $x$ is

A current carrying circular coil of radius 'R' produces magnetic field $B_1$ at an axial point P at a distance 'x' from its centre and $B_2$ at point Q placed at its centre respectively. If $B_2 = 8B_1$, the value of x is

Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have common axis. The current through $P$ and $Q$ are $I$ and $4I$ respectively in clockwise direction as seen from $O$. The net magnetic field at $O$ is:

A current $I_0$ flows through a metallic circular loop of radius $r$ as shown in the figure. Resistance of the segment $ABC$ is half that of $ADC$. Magnitude of magnetic field at the centre $O$ of the loop is:

Two circular coils X (smaller) and Y (bigger), each having a single turn, carry equal currents in the same direction and subtend the same angle at point 'O' along the axis of the coil. The distances of the centers of coil to point 'O' are $d$ and $\left(\frac{d}{2}\right)$ for coil Y and X respectively. The radii of coils Y and X are $(2r)$ and $(r)$ respectively. The magnetic induction due to the bigger coil at point 'O' is $B_y$ and that due to smaller coil X at point 'O' is $B_x$. ($d \gg r$) The relation between $B_x$ and $B_y$ is

A circular coil of wire consisting of ' $n$ ' tums each of radius 8 cm carries a current of 0.4 A. The magnitude of the magnetic field at the centre of coil is $3.14 \times 10^{-4}\text{ T}$. The value of ' $n$ ' is [Take $\mu_0 = 12.56 \times 10^{-7}$ SI unit]

A circular coil carrying current ' I ' has a radius ' $r$ ' and ' $n$ ' turns. The magnetic field along the axis of a coil at a distance ' $2\sqrt{2}\, r$ ', from its centre is ( $\mu_0 =$ permeability of free space, $n$ is very small)

An element $\overrightarrow{\Delta l} = \Delta x\, \hat{i}$ is placed at the origin and carries a current of 10 A. The magnitude of magnetic field on the Y axis at a distance of 0.5 m if $\Delta x = 1\text{ cm}$ is $\left(\frac{\mu_0}{4\pi} = 10^{-7}\right.$ SI unit $)\ (\sin 90^\circ = 1)$

A coil having 9 turns carrying current produces magnetic field $B_1$ at the centre. Now that coil is rewounded into 3 turns carrying same current. Then magnetic field at the centre $B_2$ is

A long wire carrying a steady current is bent into a circle of single turn. The magnetic field at the centre of the coil is ' B '. If it is bent into a circular loop of radius ' $r_1$ ' having ' n ' turns, the magnetic field at the centre of the coil for same current is

An electron moves in Bohr orbit. The magnetic field at the centre is proportional to

A particle carrying a charge equal to 1000 times the charge on an electron, is rotating one rotation per second in a circular path of radius ' $r$ ' $m$. If the magnetic field produced at the centre of the path is $x$ times the permeability of vacuum, the radius ' r ' in m is $\left[e = 1.6 \times 10^{-19}\text{ C}\right]\ \left[x = 2 \times 10^{-16}\right]$

A circular coil carrying current has radius ' $R$ '. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{27}$ th of its value at the centre of the coil is

Let $B_1$ be the magnitude of magnetic field at center of a circular coil of radius $R$ carrying current I. Let $B_2$ be the magnitude of magnetic field at an axial distance ' $x$ ' from the center. For $x : R = 3 : 4,\ \frac{B_2}{B_1}$ is:

The wire loop PQRSP formed by joining two semicircular wire of radii $R_1$ and $R_2$ carries a current $I$ as shown. The magnitude of the magnetic field at the centre ' O ' is

A loop ABCDA, carrying current $I = 12\text{ A}$, is placed in a plane, consists of two semi-circular segments of radius $R_1 = 6\pi\text{ m}$ and $R_2 = 4\pi\text{ m}$. The magnitude of the resultant magnetic field at center O is $k \times 10^{-7}\text{ T}$. The value of k is_________.

( Given $\mu_0 = 4\pi \times 10^{-7}\text{ T m A}^{-1}$)

Two current carrying identical coils are kept as shown in figure. The magnetic field at centre ' O ' is ( N and R represent the number of turns and radius of each coil respectively, $\mu_0 =$ permeability of free space)

Given below are two statements:

Statement (I): When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account

Statement (II): Ampere's circuital law does not depend on Biot-Savart's law.

In the light of the above statements, choose the correct answer from the options given below:

A tightly wound 100 turns coil of radius $10\text{ cm}$ carries a current of $7\text{ A}$. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4\pi \times 10^{-7}\text{ SI}$ units):

A particle carrying a charge equal to 100 times the charge on an electron is rotating one rotation per second in a circular path of radius 0.8 m. The value of magnetic field produced at the centre will be ( $\mu_0 =$ permeability of vacuum)

An arc of a circle of radius ' $R$ ' subtends an angle $\frac{\pi}{2}$ at the centre. It carries a current $I$. The magnetic field at the centre will be ( $\mu_0 =$ permeability of free space)

A current 'I' flows in anticlockwise direction in a circular arc of a wire having $\left(\frac{3}{4}\right)$th of circumference of a circle of radius R. The magnetic field ' $B$ ' at the centre of circle is ( $\mu_0 =$ permeability of free space)

A circular arc of radius r carrying current ' I ' subtends an angle $\frac{\pi}{8}$ at its centre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is ( $\mu_0 =$ permeability of free space)

Two coils P and Q each of radius R carry currents I and $\sqrt{8}\, I$ respectively in same direction. Those coils are lying in perpendicular planes such that they have a common centre. The magnitude of the magnetic field at the common centre of the two coils is ( $\mu_0 =$ permeability of free space)

Two concentric circular coils A and B having radii 20 cm and 10 cm respectively lie in the same plane. The current in coil A is 0.5 A in anticlockwise direction. The current in coil B, so that net magnetic field at the common centre is zero, is

Two identical current carrying coils with same centre are placed with their planes perpendicular to each other. If current $I = \sqrt{2}\text{ A}$ and radius of the coil is $R = 1\text{ m}$, then magnetic field at centre is equal to ( $\mu_0 =$ permeability of free space)

An element $\Delta l = \Delta x\, \hat{i}$ is placed at the origin and carries a large current $I = 10\text{ A}$. The magnetic field on the $y$-axis at a distance of $0.5\text{ m}$ from the elements $\Delta x$ of $1\text{ cm}$ length is:

A thin ring of radius ' $R$ ' carries a uniformly distributed charge. The ring rotates at constant speed ' $N$ ' r.p.s. about its axis perpendicular to the plane. If ' $B$ ' is the magnetic field at the centre, the charge on the ring is ( $\mu_0 =$ permeability of free space)

A particle having a charge 50 e is revolving in a circular path of radius 0.4 m with $1\text{ r.p.s}$. The magnetic field produced at the centre of the circle is $(\mu_0 = 4\pi \times 10^{-7}$ SI units and $e = 1.6 \times 10^{-19}\text{ C}$)

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_1 = 2\pi\text{ m}$ and $R_2 = 4\pi\text{ m}$, carrying current $I = 4\text{ A}$ as per figure given below is $\alpha \times 10^{-7}\text{ T}$. The value of $\alpha$ is ________. (Centre $O$ is common for all segments)

Two insulated circular loops A and B of radius '$a$' carrying a current of '$I$' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be:

Two circular coils $P$ and $Q$ of 100 turns each have same radius of $\pi\text{ cm}$. The currents in $P$ and $Q$ are $1\text{ A}$ and $2\text{ A}$ respectively. $P$ and $Q$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{x}\text{ mT}$, where $x =$ __________.

[Use $\mu_0 = 4\pi \times 10^{-7}\text{ T m A}^{-1}$ ]

The magnetic field at the centre of a circular coil of radius '$R$', carrying current $2A$ is '$B_1$ '. The magnetic field at the centre of another coil of radius '$3R$' carrying current $4A$ is '$B_2$'. The ratio $B_1 : B_2$ is

A circular loop of radius $r$ is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is:

A circular arc of radius '$r$' carrying current '$I$' subtends an angle $\frac{\pi}{16}$ at its centre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is $[\mu_0 =$ permeability of free space]

A straight wire carrying a current of $14\text{ A}$ is bent into a semi-circular arc of radius $2.2\text{ cm}$ as shown in the figure. The magnetic field produced by the current at the centre $(O)$ of the arc. is ____________ $\times 10^{-4}\text{ T}$

Two concentric circular coils A and B have radii $20\text{ cm}$ and $10\text{ cm}$ respectively lie in the same plane. The current in coil A is $0.5\text{ A}$ in anticlockwise direction. The current in coil B so that net field at the common centre is zero, is

Two similar coils each of radius $R$ are lying concentrically with their planes at right angles to each other. The current flowing in them are I and 2I. The resultant magnetic field of induction at the centre will be $(\mu_0 =$ Permeability of vacuum)

Two identical circular wires of radius $20\text{ cm}$ and carrying current $\sqrt{2}\text{ A}$ are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is __________ $\times 10^{-8}\text{ T}$.

(Take $\pi = 3.14$)

A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having $n$ turns. If the same current passes in both the cases, the ratio of magnetic fields produced at the centre for one turn to that of $n$ turns is

Two circular coils made from same wire but radius of $1$st coil is twice that of $2$nd coil. If magnetic field at their centres is same then ratio of potential difference applied across them is ($1$st to $2$nd coil)

A long conducting wire having a current I flowing through it, is bent into a circular coil of $N$ turns. Then it is bent into a circular coil of $n$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is:

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be:

An electron makes a full rotation in a circle of radius $0.8\text{ m}$ in one second. The magnetic field at the centre of the circle is $(\mu_0 = 4\pi \times 10^{-7}$ SI units)

An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76 \times 10^{6}\text{ m s}^{-1}$ in an orbit of radius $0.52\ \mathring{\text{A}}$. The magnetic field produced at the nucleus of the hydrogen atom is _________ T.

A circular current carrying coil has radius $R$. The magnetic induction at the centre of the coil is $B_C$. The magnetic induction of the coil at a distance $\sqrt{3}R$ from the centre along the axis is $B_A$. The ratio $B_A : B_C$ is

A circular coil of radius '$r$' and number of turns ' $n$ ' carries a current '$I$'. The magnetic fields at a small distance '$h$' along the axis of the coil $(B_a)$ and at the centre of the coil $(B_c)$ are measured. The relation between $B_c$ and $B_a$ is

The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field at distance $r$ from the centre of coil on its axis is $\sqrt{x} : 1$. The value of $x$ is __________

Figure shows two semicircular loops of radii $R_1$ and $R_2$ carrying current $I$. The magnetic field at the common centre '$O$' is

Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are $20\text{ cm}$ and $40\text{ cm}$ and they carry respectively $0.2\text{ A}$ and $0.3\text{ A}$ current in opposite direction. The magnetic field at the centre is ($\mu_0 = 4\pi \times 10^{-7}$ SI units)

A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve $z$ direction and lying in $xy$ plane is shown in figure. The plot of $\hat{j}$ component of magnetic field (By) at a distance '$a$' (less than radius of the coil) and on $yz$ plane vs $z$ coordinate looks like

The shape of the magnetic field lines due to an infinite long, straight current carrying conductor is

Given below are two statements:

Statement I: Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only.

Statement II: Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q.

In light of above statements choose the most appropriate answer from the options given below.

A closely packed coil having 1000 turns has an average radius of 62.8 cm. If current carried by the wire of the coil is 1 A, the value of magnetic field produced at the centre of the coil will be (permeability of free space $= 4\pi \times 10^{-7}$ H/m) nearly

$B_X$ and $B_Y$ are the magnetic fields at the centre of two coils $X$ and $Y$ respectively each carrying equal current. If coil $X$ has 200 turns and $20\text{ cm}$ radius and coil $Y$ has 400 turns and $20\text{ cm}$ radius, the ratio of $B_X$ and $B_Y$ is:

A closely wound circular coil of radius 5 cm produces a magnetic field of $37.68 \times 10^{-4}\text{ T}$ at its center. The current through the coil is _________A.

[Given, number of turns in the coil is 100 and $\pi = 3.14$]

The magnetic field on the axis of a circular loop of radius 100 cm carrying current $I = \sqrt{2}\text{ A}$, at point 1 m away from the centre of the loop is given by:

The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction B2 at its centre. The ratio of $\frac{B_2}{B_1}$ is

The magnetic field at the center of current carrying circular loop is $B_1$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_2$. The value of $B_1/B_2$ will be

The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance $\frac{r}{2}$ from the centre is:

A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii r1 and r2 respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be:

An electron (e) moves in circular orbit of radius 'r' with uniform speed 'V'. It produces magnetic field 'B' at the centre of circle. The magnetic field B is $(\mu_0 =$ permeability of free space)