Magnetic Effects of Current and Magnetism — JEE Main PYQs

A particle having charge $10^{-9}$ C moving in $x$-$y$ plane in fields of $0.4\,\hat{j} \text{ N/C}$ and $4 \times 10^{-3}\,\hat{k}$ T experiences a force of $\left(4\hat{i} + 2\hat{j}\right) \times 10^{-10}$ N. The velocity of the particle at that instant is ________ m/s.

An insulated wire is wound so that it forms a flat coil with $N = 200$ turns. The radius of the innermost turn is $r_1 = 3$ cm, and of the outermost turn $r_2 = 6$ cm. If 20 mA current flows in it then the magnetic moment will be $\alpha \times 10^{-2} \text{ A.m}^2$. The value of $\alpha$ is _____.

A solenoid has a core made of material with relative permeability 400. The magnetic field produced in the interior of solenoid is $1.0 \text{ T}$. The magnetic intensity in SI units is $\alpha \times 10^5$. The value of $\alpha$ is ________.

(Free space permeability $\mu_0 = 4\pi \times 10^{-7}$ SI units.)

Two identical small bar magnets each of dipole moment $3\sqrt{5} \text{ J/T}$ are placed at a center to center separation of $10 \text{ cm}$, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point $P$ midway between the magnets is $\alpha \times 10^{-3} \text{ T}$. The value of $\alpha$ is _______.

($\mu_0 = 4\pi \times 10^{-7} \text{ Tm/A}$)

[Figure: Two bar magnets 10 cm apart center to center. The left magnet (S-N) lies horizontally with its axis along the line joining the magnets; the right magnet (S on top, N at bottom) is oriented vertically, perpendicular to that line. Point P is midway between them on the line.]

A circular coil of radius $2 \text{ cm}$ and $125$ turns carries a current of $1 \text{ A}$. The coil is placed in a uniform magnetic field of magnitude $0.4 \text{ T}$. The axis of the coil makes an angle of $30°$ with the direction of the magnetic field. The torque acting on the coil is $\alpha \times 10^{-4} \text{ N·m}$. The value of $\alpha$ is __________.

($\pi = 3.14$)

The charged particle moving in a uniform magnetic field of $\left(3\hat{i} + 2\hat{j}\right) \text{T}$ has an acceleration $\left(4\hat{i} - \dfrac{x}{2}\hat{j}\right) \text{m/s}^2$. The value of $x$ is

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v} = \left( \dfrac{v_0}{\sqrt{2}}\, \hat{x} + \dfrac{v_0}{\sqrt{2}}\, \hat{y} \right)$. There exists a uniform magnetic field $\vec{B} = B_0\, \hat{z}$ and a space varying electric field $\vec{E} = E_0\, e^{-\lambda x}\, \hat{x}$ within the region $0 \leq x \leq L$. After travelling a distance such that $x$-coordinate has changed from $x = 0$ to $x = L$, the change in the kinetic energy 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 $\alpha \times 10^{-14}$ J. The value of $\alpha$ is ________.

($\mu_o = 4\pi \times 10^{-7}\ \text{Tm/A}$, $\pi = 3.14$)

A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm. The magnetic field at the mid point between the two wires is ______ $\mu$T. ($\dfrac{\mu_0}{4\pi} = 10^{-7}$ N/A$^2$)

A current carrying circular loop of radius $2\,\text{cm}$ with unit normal $\hat{n} = \dfrac{\hat{k} + \hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B} = B_0\left(3\hat{i} + 2\hat{k}\right)$. If $B_0 = 4 \times 10^{-3}\,\text{T}$ and current $I = 100\sqrt{2}\,\text{A}$, the torque experienced by the loop is ________ $\text{Wb.A}$. ($\pi = 3.14$)

A $5\,\text{mg}$ particle carrying a charge of $5\pi \times 10^{-6}\,\text{C}$ is moving with velocity of $\left(3\hat{i} + 2\hat{k}\right) \times 10^{-2}\,\text{m/s}$ in a region having magnetic field $\vec{B} = 0.1\,\hat{k}\,\text{Wb/m}^2$. It moves a distance of $\alpha$ meter along $\hat{k}$ when it completes 5 revolutions. The value of $\alpha$ is ________.

The relationship between the magnetic susceptibility $(\chi)$ and the magnetic permeability $(\mu)$ is given by :

($\mu_0$ is the permeability of free space and $\mu_r$ is relative permeability)

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 $x:R=3:4$, $\dfrac{B_2}{B_1}$ is :

In a moving coil galvanometer, two moving coils $M_1$ and $M_2$ have the following particulars :

$R_1 = 5~\Omega,\ N_1 = 15,\ A_1 = 3.6\times10^{-3}~\mathrm{m^2},\ B_1 = 0.25~\mathrm{T}$

$R_2 = 7~\Omega,\ N_2 = 21,\ A_2 = 1.8\times10^{-3}~\mathrm{m^2},\ B_2 = 0.50~\mathrm{T}$

Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_1$ and $M_2$ ?

A 4.0 cm long straight wire carrying a current of 8A is placed perpendicular to a uniform magnetic field of strength 0.15 T. The magnetic force on the wire is __________ mN.

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

(Given $\mu_0 = 4\pi \times 10^{-7} \ \mathrm{Tm\,A^{-1}}$)

[Figure: two concentric semicircles above the line A–B–O–C–D; outer semicircle of radius $R_1$ from A to D and inner semicircle of radius $R_2$ from B to C, joined by straight segments A–B and C–D along the diameter, with current I flowing along the loop ABCDA]

A magnetic dipole experiences a torque of $80\sqrt{3}$ N m when placed in uniform magnetic field in such a way that dipole moment makes angle of 60° with magnetic field. The potential energy of the dipole is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : If Oxygen ion ($\mathrm{O^{-2}}$) and Hydrogen ion ($\mathrm{H^+}$) enter normal to the magnetic field with equal momentum, then the path of $\mathrm{O^{-2}}$ ion has a smaller curvature than that of $\mathrm{H^+}$.

Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.

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

A particle of charge $1.6 \mathrm{~\mu C}$ and mass $16 \mathrm{~\mu g}$ is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is ________ s. ($\pi = 3.14$)

A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E?

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $\chi_{\mathrm{Mg}} = 1.2 \times 10^{-5}$) is :

Uniform magnetic fields of different strengths ($\mathrm{B_1}$ and $\mathrm{B_2}$), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity $v$ and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface ?

[Figure: a horizontal interface separating Region 1 (above, field $B_1$ into the page shown by crosses) and Region 2 (below, field $B_2$ into the page shown by crosses)]

(Consider the velocity of the particle to be normal to the magnetic field and $\mathrm{B_2} > \mathrm{B_1}$)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Magnetic monopoles do not exist.

Reason (R) : Magnetic field lines are continuous and form closed loops.

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

Figure shows a current carrying square loop ABCD of edge length is '$a$' lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is

[Figure: square loop ABCD oriented as a diamond with current I entering at A (left) and leaving at C (right); current $i_1$ flows through the upper path ABC and $i_2$ through the lower path ADC; edge length $a$]

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2 \times 10^5\ \mathrm{ms^{-1}}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x \times 10^4\ \mathrm{N/C}$. The value of $x$ is __________. Take the mass of the proton $= 1.6 \times 10^{-27}\ \mathrm{kg}$.

Consider a moving coil galvanomenter (MCG):

A. The torsional constant in moving coil galvanometer has dimentions $[\mathrm{ML^2T^{-2}}]$

B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.

C. If we increase number of turns (N) to its double (2N), then the voltage sensitivity doubles.

D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.

E. Current sensitivity of MCG depends inversely on number of turns of coil.

Choose the correct answer from the options given below:

A galvanometer having a coil of resistance $30~\Omega$ need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $\frac{30}{X}~\Omega$, where X is

A current of 5A exists in a square loop of side $\frac{1}{\sqrt{2}}$ m. Then the magnitude of the magnetic field B at the centre of the square loop will be $p \times 10^{-6}$ T. where, value of p is _____. [Take $\mu_0 = 4\pi \times 10^{-7}~\mathrm{T\,m\,A^{-1}}$].

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.

Reason (R) : The magnetic field in that region is along the direction of velocity of the electron.

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

A long straight wire of circular cross-section of radius 'a' carries a steady current I. The current I is uniformly distributed across this cross-section. The variation of magnitude of magnetic field B with distance r from the centre of the wire is represented by the graph :

N charges, each of value q, are placed at equal intervals on a circle of radius R. The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A relatively large Amperian loop B encircles the whole circle whereas a relatively small Amperian loop A encircles a small segment. The difference between the enclosed currents, $I_A - I_B$, for the given Amperian loops is

[Figure: a circle of radius R carrying N equally spaced charges, rotating with angular velocity ω about its axis; a large Amperian loop B threads the entire circle while a small Amperian loop A encircles a small segment of it]

A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is ______.

$\left[\text{Take mass of electron } m_e = 9 \times 10^{-31}\ \mathrm{kg}, \text{ charge of electron } |q_e| = 1.6 \times 10^{-19}\ \mathrm{C}, \ \mu_0 = 4\pi \times 10^{-7}\ \mathrm{\frac{N}{A^2}}, \ 1\ \mathrm{ns} = 10^{-9}\ \mathrm{s}\right]$

Consider a long thin conducting wire carrying a uniform current I. A particle having mass "M" and charge "q" is released at a distance "$a$" from the wire with a speed $v_o$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance $x$ from the wire. The value of $x$ is

[$\mu_0$ is the permeability of vacuum]

[Figure: an infinite straight wire carrying current I along the horizontal, which forms a circular bend (loop) of radius $a$ around the origin O; the arc subtends the region above and to the left of O, and the two straight portions extend to infinity on the right]

An infinite wire has a circular bend of radius $a$, and carrying a current I as shown in figure. The magnitude of magnetic field at the origin O of the arc is given by :

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

The magnetic field existing in a region is given by $\vec{\mathrm{B}} = 0.2(1 + 2x)\hat{k}~\mathrm{T}$. A square loop of edge 50 cm carrying 0.5 A current is placed in $x$-$y$ plane with its edges parallel to the $x$-$y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is ________ mN.

[Figure: x-y coordinate axes with a square loop located at x = 2 m, y = 2 m, its sides parallel to the axes and current circulating around it as marked by arrows]

The magnetic moment of a bar magnet is $0.5~\mathrm{Am^2}$. It is suspended in a uniform magnetic field of $8\times 10^{-2}~\mathrm{T}$. The work done in rotating it from its most stable to most unstable position is:

Two parallel long current carrying wire separated by a distance $2r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is ______.

[Figure: two vertical parallel wires carrying currents $I$ (left wire) and $2I$ (right wire), separated by distance $2r$ with midpoint $O$; point $A$ lies at distance $r$ to the left of the left wire, and point $C$ lies at distance $r$ to the right of the right wire]

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

A 2A current carrying straight metal wire of resistance $1\ \Omega$, resistivity $2 \times 10^{-6}\ \Omega\mathrm{m}$, area of cross-section $10\ \mathrm{mm}^2$ and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$. The magnitude of B is ________ $\times 10^{-1}$ T (given, $g = 10\ \mathrm{m/s^2}$).

The electrostatic force $\left(\vec{F}_1\right)$ and magnetic force $\left(\vec{F}_2\right)$ acting on a charge q moving with velocity $v$ can be written :

A galvanometer of resistance $100\ \Omega$ when connected in series with $400\ \Omega$ measures a voltage of upto 10 V. The value of resistance required to convert the galvanometer into ammeter to read upto 10 A is $x \times 10^{-2}\ \Omega$. The value of $x$ is :

A solenoid of length 0.5 m has a radius of 1 cm and is made up of 'm' number of turns. It carries a current of 5 A. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3}\ \mathrm{T}$ then the value of m is ________.

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

[Figure: current element $\Delta x$ along the x-axis at the origin; point $P$ on the y-axis at a distance $0.5\,m$ above the element]

A circular coil having 200 turns, $2.5\times10^{-4}\ \mathrm{m^2}$ area and carrying $100\ \mu A$ current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^\circ$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$, is _________ $\mu J$.

Match List-I with List-II :

List-I (Y vs X) | List-II (Shape of Graph)

(A) Y = magnetic susceptibility, X = magnetising field — (I) [Figure: straight line through origin with positive slope]

(B) Y = magnetic field, X = distance from centre of a current carrying wire for $x < a$ (where a = radius of wire) — (II) [Figure: curve starting flat at high Y then falling off sharply at large X]

(C) Y = magnetic field, X = distance from centre of a current carrying wire for $x > a$ (where a = radius of wire) — (III) [Figure: horizontal line, Y constant with X]

(D) Y = magnetic field inside solenoid, X = distance from centre — (IV) [Figure: curve decreasing steeply then levelling off near zero (hyperbola-like decay)]

Choose the correct answer from the options given below :

A coil having 100 turns, area of $5 \times 10^{-3}\ \mathrm{m^2}$, carrying current of 1 mA is placed in uniform magnetic field of 0.20 T such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90°$ is ________ μJ.

Paramagnetic substances:

A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field.

Choose the most appropriate answer from the options given below:

An electron with kinetic energy 5 eV enters a region of uniform magnetic field of $3\ \mu\mathrm{T}$ perpendicular to its direction. An electric field E is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is _____ $\mathrm{NC^{-1}}$.

(Given, mass of electron $= 9 \times 10^{-31}$ kg, electric charge $= 1.6 \times 10^{-19}$ C)

A long straight wire of radius $a$ carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ from axis of the wire is :

The coercivity of a magnet is $5 \times 10^3$ A/m. The amount of current required to be passed in a solenoid of length 30 cm and the number of turns 150, so that the magnet gets demagnetised when inside the solenoid is _________ A.

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 square loop of edge length 2 m carrying current of 2 A is placed with its edges parallel to the $x$-$y$ axis. A magnetic field is passing through the $x$-$y$ plane and expressed as $\vec{B} = B_0(1 + 4x)\hat{k}$, where $B_0 = 5$ T. The net magnetic force experienced by the loop is ________ N.

A proton and a deutron ($q = +e$, $m = 2.0\mathrm{u}$) having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is :

A straight magnetic strip has a magnetic moment of 44 $\mathrm{Am^2}$. If the strip is bent in a semicircular shape, its magnetic moment will be ________ $\mathrm{Am^2}$.

(given $\pi = \frac{22}{7}$)

A galvanometer has a resistance of 50 $\Omega$ and it allows maximum current of 5 mA. It can be converted into voltmeter to measure upto 100 V by connecting in series a resistor of resistance :

A regular polygon of 6 sides is formed by bending a wire of length $4\pi$ meter. If an electric current of $4\pi\sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{-7}$ T. The value of $x$ is ________.

In an ammeter, 5% of the main current passes through the galvanometer. If resistance of the galvanometer is G, the resistance of ammeter will be :

A moving coil galvanometer has 100 turns and each turn has an area of 2.0 $\mathrm{cm}^2$. The magnetic field produced by the magnet is 0.01 T and the deflection in the coil is 0.05 radian when a current of 10 mA is passed through it. The torsional constant of the suspension wire is $x \times 10^{-5}$ N-m/rad. The value of $x$ is ________.

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec{E}$ and $\vec{B}$ represent the electric and magnetic fields respectively, then the region of space may have :

(A) $E = 0,\ B = 0$

(B) $E = 0,\ B \neq 0$

(C) $E \neq 0,\ B = 0$

(D) $E \neq 0,\ B \neq 0$

Choose the most appropriate answer from the options given below :

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is 5.0 cm. The magnitude of the magnetic field at a point P midway between the wires is ________ $\mu$T. (Given : $\mu_0 = 4\pi \times 10^{-7}\ \mathrm{TmA^{-1}}$)

[Figure: two vertical parallel wires each carrying 10 A, the left wire's current directed upward and the right wire's current directed downward, with point P midway between them]

A galvanometer having coil resistance $10\,\Omega$ shows a full scale deflection for a current of 3 mA. For it to measure a current of 8 A, the value of the shunt should be:

The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of $24\,\Omega$ is applied. The resistance of galvanometer coil will be :

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of 20 cm from its center is $1.5 \times 10^{-5}\ T\,m$. The magnetic moment of the dipole is ________ $A\,m^2$. (Given : $\frac{\mu_o}{4\pi} = 10^{-7}\ T\,m\,A^{-1}$)

Two insulated circular loop 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 :

[Figure: two circular loops of equal radius with a common centre O, loop A horizontal and loop B vertical (mutually perpendicular planes), each carrying current I anticlockwise]

The horizontal component of earth's magnetic field at a place is $3.5 \times 10^{-5}~\mathrm{T}$. A very long straight conductor carrying current of $\sqrt{2}~\mathrm{A}$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is ________ $\times 10^{-6}~\mathrm{N/m}$.

The current of $5A$ flows in a square loop of sides $1\ m$ is placed in air. The magnetic field at the centre of the loop is $X\sqrt{2} \times 10^{-7}\ T$. The value of $X$ is ________.

A rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $B = B_0\,\hat{j}$ as shown in figure. The magnetic force on the wire if it has a current $i$ is:

[Figure: U-shaped wire with semicircular top of radius R inside a region of magnetic field pointing out of the page (dots), with x–y axes shown; the two straight sections extend downward out of the field region]

An electron moves through a uniform magnetic field $\vec{B} = B_0\,\hat{i} + 2B_0\,\hat{j}\ T$. At a particular instant of time, the velocity of electron is $\vec{u} = 3\hat{i} + 5\hat{j}\ \mathrm{m/s}$. If the magnetic force acting on electron is $\vec{F} = 5e\,\hat{k}\ N$, where $e$ is the charge of electron, then the value of $B_0$ is ________ $T$.

A uniform magnetic field of $2 \times 10^{-3}\ T$ acts along positive $Y$-direction. A rectangular loop of sides 20 cm and 10 cm with current of $5\ A$ is in $Y$–$Z$ plane. The current is in anticlockwise sense with reference to negative $X$ axis. Magnitude and direction of the torque is:

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

[Use $\mu_0 = 4\pi \times 10^{-7}\ TmA^{-1}$]