Moving Charges and Magnetism PYQs

A 100-turn closely wound circular coil of radius 5 cm has a magnetic field of 3.14 × 10⁻³ T at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively: (Take μ₀ = 4π × 10⁻⁷ T m/A)

A galvanometer of resistance 100 Ω gives full scale deflection for a current of 1 mA. It is converted into an ammeter of range 0–10 A. The shunt required is:

The figure given below shows a long straight solid wire of circular cross-section of radius 'a' carrying steady current I. The current I is uniformly distributed across its cross-section. The plot which correctly represents the variation of magnetic field (B) with distance (r) from the axis of the conductor in the region is:

An electron (mass $9\times10^{-31}\,\text{kg}$ and charge $1.6\times10^{-19}\,\text{C}$) moving with speed $\dfrac{c}{100}$ ($c$ = speed of light) is injected into a magnetic field $\vec{B}$ of magnitude $9\times10^{-4}\,\text{T}$ perpendicular to its direction of motion. We wish to apply a uniform electric field $\vec{E}$ together with the magnetic field so that the electron does not deflect from its path. Then ($c = 3\times10^8\,\text{m s}^{-1}$)

A 2 amp current is flowing through two different small circular copper coils having radii ratio 1:2. The ratio of their respective magnetic moments will be :

A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e) where n is an integer, h is Planck’s constant and e is the magnitude of electron’s charge. According to the model, the magnetic moment of an electron in its lowest energy state will be (m is the mass of the electron)

In a uniform magnetic field of $0.049\,\text{T}$, a magnetic needle performs $20$ complete oscillations in $5\,\text{s}$ as shown. The moment of inertia of the needle is $9.8\times10^{-6}\,\text{kg m}^2$. If the magnetic moment of the needle is $x\times10^{-5}\,\text{A m}^2$, then the value of $x$ is:

Match List-I with List-II. Choose the correct answer from the options given below:

A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as 4π × 10⁻⁷ SI units):

A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to: A. hold the sheet there if it is magnetic. B. hold the sheet there if it is non-magnetic. C. move the sheet away from the pole with uniform velocity if it is conducting. D. move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar. Choose the correct statement(s) from the options given below:

An iron bar of length $L$ has magnetic moment $M$. It is bent at the middle of its length such that the two arms make an angle $60^\circ$ with each other. The magnetic moment of this new magnet is:

A wire carrying a current $I$ along the positive $x$-axis has length $L$. It is kept in a magnetic field $\vec{B} = (2\hat{i} + 3\hat{j} - 4\hat{k})\,\text{T}$. The magnitude of the magnetic force acting on the wire is:

A very long conducting wire is bent in a semi-circular shape from A to B as shown in the figure. The magnetic field at point P for steady current configuration is given by:

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 I(dl) 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, I(dl), 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.

The dimensions [MLT⁻²A⁻²] belong to the:

A square loop of side 1 m and resistance 1 Ω is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is:

A long solenoid of radius 1 mm has 100 turns per mm. If 1 A current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field inside and outside region of the wire is:

An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of 10⁵ m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

A thick current carrying cable of radius R carries current I uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance r from the axis of the cable is represented by

In the product: $\vec{F} = q(\vec{v} \times \vec{B})$ $= q\,\vec{v} \times (B\hat{i} + B\hat{j} + B_0\hat{k})$ For $q = 1$ and $\vec{v} = 2\hat{i} + 4\hat{j} + 6\hat{k}$ and $\vec{F} = 4\hat{i} - 20\hat{j} + 12\hat{k}$ what will be the complete expression for $\vec{B}$?

A uniform conducting wire of length 12a and resistance R is wound up as a current carrying coil in the shape of: (i) an equilateral triangle of side 'a', (ii) a square of side 'a'. The magnetic dipole moments of the coil in each case respectively are:

A magnetic material has magnetic susceptibility 1999. It is subjected to a magnetising field of 1200 A m⁻¹. The permeability of the material of the rod is : (μ₀ = 4π × 10⁻⁷ T m A⁻¹)

A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is : (μ$_0$ = 4π × 10⁻⁷ T m A⁻¹)

The relations amongst the three elements of earth’s magnetic field, namely horizontal component H, vertical component V and dip δ are, ($B_E$ = total magnetic field)

Two toroids 1 and 2 have total number of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry same current i, the ratio of the magnetic fields along the two loops is

A straight conductor carrying current $i$ splits into two parts as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre $P$ of the loop is

Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is:

A metallic rod of mass per unit length 0.5 kg m⁻¹ is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is:

An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying same current $I$ along the same direction is shown in figure. Magnitude of force per unit length on the middle wire $B$ is given by

A $250$-turn rectangular coil of length $2.1\ \text{cm}$ and width $1.25\ \text{cm}$ carries a current of $85\ \mu\text{A}$ and is subjected to a magnetic field of $0.85\ \text{T}$. Work done for rotating the coil by $180^{\circ}$ against the torque is

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is $B$. If it is bent into a circular coil of $n$ turns, the magnetic field at the centre of this coil of $n$ turns will be:

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by $60^\circ$ is $W$. Now the torque required to keep the magnet in this new position is:

An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 × 10⁻² T. If the value of e/m is 1.76 × 10¹¹ C/kg, the frequency of revolution of the electron is:

A rectangular coil of length $0.12\,\text{m}$ and width $0.10\,\text{m}$ having $50$ turns of wire is suspended vertically in a uniform magnetic field of strength $0.2\,\text{Wbm}^{2}$. The coil carries a current of $2\,\text{A}$. If the plane of the coil is inclined at an angle of $30^{\circ}$ with the direction of the magnetic field, the torque required to keep the coil in stable equilibrium will be:

A proton and an alpha particle both enter a region of uniform magnetic field $B$, moving at right angles to the field. If the radii of circular orbits for both the particles are equal and the kinetic energy acquired by the proton is $1\,\text{MeV}$, then the energy acquired by the alpha particle will be:

Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment $\vec{m}$. Which configuration has highest net magnetic dipole moment?

In an ammeter 0.2% of main current passes through the galvanometer. If resistance of galvanometer is G, the resistance of ammeter will be:

Two identical long conducting wires AOB and COD are placed at right angles to each other, with one above the other such that O is their common point. The wires carry currents I₁ and I₂ respectively. Point P lies at a distance d from O along a direction perpendicular to the plane containing the wires. The magnetic field at point P will be:

When a proton is released from rest in a room, it starts with an initial acceleration $a_0$ towards west. When it is projected towards north with speed $v_0$, it moves with an initial acceleration $3a_0$ towards west. The electric and magnetic fields in the room are

A current loop in a magnetic field

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in a uniform magnetic field. What should be the energy of an $\alpha$-particle to describe a circle of same radius in the same field?

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I₁ at a distance d from the conductor as shown in figure. The loop will experience:

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency f Hz. The magnitude of magnetic induction at the centre of the ring is:

A short bar magnet of magnetic moment 0.4 J T⁻¹ is placed in a uniform magnetic field of 0.16 T. The magnet is in stable equilibrium when the potential energy is:

A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is i. The resultant magnetic field due to the two semicircular parts at their common centre is

A closely wound solenoid of 2000 turns and area of cross-section $1.5 \times 10^{-4}\,m^2$ carries a current of $2.0\,A$. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field $5 \times 10^{-2}\,T$. The magnetic angle of dip is $30^{\circ}$ with the axis of the solenoid. The torque on the solenoid will be

A particle having a mass of $10^{-2}\,kg$ carries a charge of $5 \times 10^{-8}\,C$. The particle is given an initial horizontal velocity of $10^5\,ms^{-1}$ in the presence of electric field $\vec{E}$ and magnetic field $\vec{B}$. To keep the particle moving in a horizontal direction, it is necessary that (i) $\vec{B}$ should be perpendicular to the direction of velocity and $\vec{E}$ should be along the direction of velocity. (ii) Both $\vec{B}$ and $\vec{E}$ should be along the direction of velocity. (iii) Both $\vec{B}$ and $\vec{E}$ are mutually perpendicular and perpendicular to the direction of velocity. (iv) $\vec{B}$ should be along the direction of velocity and $\vec{E}$ should be perpendicular to the direction of velocity. Which one of the following pairs of statements is possible?

The magnetic moment of a diamagnetic atom is:

Two identical bar magnets are fixed with their centres at a distance d apart. A stationary charge Q is placed at P in between the two magnets at a distance D from the centre O as shown in the figure. The force on the charge Q is:

A bar magnet having a magnetic moment of $2\times10^4\,JT^{-1}$ is free to rotate in a horizontal plane. A horizontal magnetic field $B=6\times10^{-4}\,T$ exists in the space. The work done in rotating the magnet slowly from a direction parallel to the field to a direction $60^\circ$ from the field is:

The magnetic force acting on a charged particle of charge $-2\mu C$ in a magnetic field of $2\,T$ acting in y-direction, when the particle velocity is $(2\hat{i}+3\hat{j})\times10^6\,m/s$, is:

Under the influence of a uniform magnetic field, a charged particle moves with constant speed V in a circle of radius $R$. The time period of rotation of the particle:

If a diamagnetic substance is brought near the north or the south pole of a bar magnet, it is:

A particle of mass m, charge Q and kinetic energy T enters a transverse uniform magnetic field of induction $\vec{B}$. After 3 seconds the kinetic energy of the particle will be

A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RQ are F₁, F₂ and F₃ respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is

A circular disc of radius 0.2 meter is placed in a uniform magnetic field of induction 1/π (Wb/m²) in such a way that its axis makes an angle of 60° with B. The magnetic flux linked with the disc is

A galvanometer of resistance 50 Ω is connected to a battery of 3 V along with a resistance of 2950 Ω in series. A full scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be

Curie temperature is the temperature above which

Find the force on the conductor carrying current i as shown in the figure.

When a charged particle moving with velocity is subjected to a magnetic field of induction $\vec{B}$, the force on it is non-zero. This implies that:

Two circular coils 1 and 2 are made from the same wire but the radius of the 1st coil is twice that of the 2nd coil. What is the ratio of potential difference applied across them so that the magnetic field at their centres is the same?

Above Curie temperature:

A coil in the shape of an equilateral triangle of side $l$ is suspended between the pole pieces of a permanent magnet such that its plane is parallel to the magnetic field $\vec{B}$. If due to a current $i$ in the triangle a torque $\tau$ acts on it, the side of the triangle is:

A very long straight wire carries a current I. At the instant when a charge +Q at point P has velocity $\vec{v}$, as shown, the force on the charge is:”

If the magnetic dipole moment of an atom of diamagnetic material, paramagnetic material and ferromagnetic material is denoted by $\mu_d$, $\mu_p$ and $\mu_f$ respectively, then

An electron moves in a circular orbit with uniform speed v. It produces a magnetic field B at the centre of the circle. The radius of the circle is proportional to: