Moving Charges and Magnetism

Lorentz magnetic force is acting on a particle of charge q moving with velocity $\vec{V}$ in a magnetic field $\vec{B}$. The work done by this force on the charged particle is

The magnetic field intensity H at the centre of a long solenoid having $n$ turns per unit length and carrying a current I, when no material is kept in it is ( $\mu_0=$ permeability of free space)

A long straight wire of radius ' $r$ ' carries a steady current ' $I$ '. The current is uniformly distributed over its cross-section. The ratio $\left(\frac{B}{B_1}\right)$ of the magnetic field ' B ' and ' $\mathrm{B}_1$ ' at radial distan...

Current $I$ is carried in a wire of length ' $L$ '. If wire is bent into a circular coil of single turn, the maximum torque in a given magnetic field $B$ is

A square of side ' $L$ ' metre lies in $x-y$ plane in a region where the magnetic field is $\overline{\mathrm{B}}$ and $\vec{B}=B_0(2 \hat{i}+3 \hat{j}+4 \hat{k})$, where $B_0$ is constant. The magnitude of flux passing through the square (...

In the following figure magnitude of the magnetic field at the point $p$ is

A circular coil carrying current ' T ' 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)

A square coil ABCD of side ' L ' is carrying a current in clockwise direction. A straight conductor carrying current $\mathrm{I}_2$ (upward direction) is kept parallel to side AB at a distance $\frac{\mathrm{L}}{3}$ in the plane of $A B C D...

The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment ( M ) of the coil is ( $\mu_0=$ permeability of free space)

Let the current ' $I$ ' be associated with an electron of charge ' $e$ ' moving in a circular orbit of radius ' $r$ ' with speed ' $v$ ' around the positively charged nucleus. The ratio $\frac{r}{v}$ is

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)

The relation between magnetic moment $(\mathrm{M})$ of a current carrying circular coil and length (L) of the wire used is

In hydrogen atom, an electron of charge 'e' revolves in an orbit of radius ' $r$ ' with speed ' $v$ '. The magnetic moment associated with electron 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 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 $3.14 \times 10^{-4} \mathrm{~T}$. The value of ' $n$ ' is
[Take $\mu_0=12.56 \...

A wire of length $L$ carries current $I$ along x - axis. A magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}) \mathrm{T}$ acts on the wire. The magnitude of magnetic force acting on ...

Two similar wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and same current is passed through them. Torque experienced by

A particle of charge $q$ moves with a velocity $\overrightarrow{\mathrm{V}}=a \hat{\mathrm{i}}$ in a magnetic field $\overrightarrow{\mathrm{B}}=b \hat{\mathrm{j}}+c \hat{\mathrm{k}}$, where ' $a$ ', ' b ' and ' c ' are constants. The magni...

Two very long straight conductors (wires) are set parallel to each other. Each carries a current ' I ' in the same direction and the separation between them is ' 2 r '. The intensity of the magnetic field at point ' P ' (as shown in the fig...

Two identical long parallel wires carry currents ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' such that $\mathrm{I}_1>\mathrm{I}_2$. When the currents are in the same direction, the magnetic field at a point midway between the wires is $8 \tim...

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

Two long parallel wires carry currents $I_1$ and $\mathrm{I}_2\left(\mathrm{I}_1>\mathrm{I}_2\right)$. When currents are flowing in the same direction, the magnetic field at a point midway between the wires is $6 \times 10^{-6} \mathrm{~T}$...

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

A wire has three different sections as shown in figure. The magnitude of the magnetic field produced at the centre ' $O$ ' of the semicircle by three sections together is ( $\mu_0=$ permiability of free space)

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 ' $\mathrm{r}_1$ ' having ' n ' turns, the magnetic field at the...

An element $\overrightarrow{\Delta l}=\Delta \mathrm{xi}$ 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 $\Delta x=1 \mathrm{~cm}$ is $\left(\frac{\mu_0}{4 \pi...

A current ' I ' is flowing in a conductor PQRST as shown in figure. The radius of curved path QRS is ' R ' and length of straight portion PQ and ST is very large. The magnetic field at the centre $[\mathrm{O}]$ of the curved part is ( $\mu_...

Two long straight wires A and B carrying equal current 'I' were kept parallel to each other at distance ' $d$ ' apart. Magnitude of magnetic force experienced by length $L$ of wire $A$ is ' $F$ '. If the distance between the wires is made h...

Two long parallel wires carrying currents 4 A and 3 A in opposite directions are placed at a distance of 5 cm from each other. A point P is at equidistance from both the wires such that the line joining the point P to the wires are perpendi...

The ratio of angular momentum $L$ of an electron to the magnetic dipole moment $\overrightarrow{\mathrm{m}}_{\text {orb }}$ is ( ' $m$ ' is mass of electron, ' $e$ ' is charge on electron)

Bohr model is applied to a particle of mass m and charge $q$ is moving in a plane under the influence of a transverse magnetic field (B). The energy of the charged particle in the second level will be ( $\mathrm{h}=$ Planck's constant)

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...

Two long conductors separated by a distance ' d ' carry currents ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' in the same directions. They exert a force ' $F$ ' on each other. The distance between them is increased to ' 3 d '. If new repulsive...

The magnetic field intensity inside current carrying solenoid is $\mathrm{H}=2.4 \times 10^3 \mathrm{~A} / \mathrm{m}$. If length and number of turns of a solenoid is 15 cm and 60 turns respectively. The current flowing in the solenoid is

The magnetic induction due to an ideal solenoid is independent of

A long solenoid carrying a current produces magnetic field B along its axis. If the number of turns per cm are tripled and the current is made $\left(\frac{1}{4}\right)^{\text {th }}$ then the new value of magnetic field will be

A current carrying circular loop of radius ' $R$ ' and current carrying long straight wire are placed in the same plane. $I_c$ and $I_w$ are the currents through circular loop and long straight wire respectively. The perpendicular distance ...

The magnetic potential energy stored in certain inductor is $64 \times 10^{-3} \mathrm{~J}$, when the current in the inductor is 80 mA . This inductor is of inductance

A massless square loop of wire of resistance ' $R$ ' supporting a mass ' M ' hangs vertically with one of its sides in a uniform magnetic field ' B ' directed outwards in the shaded region. A d.c. voltage ' V ' is applied to the loop. For w...

A charged particle is moving in a uniform magnetic field in a circular path with radius ' $R$ '. When the energy of the particle is doubled, then the new radius will be

A charged particle of charge ' $q$ ' is accelerated by a potential difference ' $V$ ' enters a region of uniform magnetic field ' $B$ ' at right angles to the direction of field. The charged particle completes semicircle of radius ' $r$ ' i...

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)

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

A current of 5 A flows through a toroid having a core of mean radius 20 cm . If 4000 turns of the conducting wire are wound on the core, then the magnetic field inside the core of the toroid is [permeability of free space $=4 \pi \times 10^...

A charged particle is moving along a magnetic field line. What is the magnetic force acting on the particle? $\left(\sin 0^{\circ}=0, \sin \frac{\pi}{2}=1\right)$

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 ( $...

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

The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment of the coil is ( $\mu_0=$ permeability of free space)

Three long, straight parallel wires carrying currents are arranged as shown. The wire C which carries a current of 5.0 A is so placed that it experiences no force. The distance of wire C from wire $D$ is

Cyclotron is used to