Moving Charges and Magnetism

Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimentions \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns \((\mathrm{N})\) to its double ( 2 N ), 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:

[JEE Main 2025, 23 Jan (Shift 1)]

A proton is moving with a uniform velocity of \(2\times 1{0}^{8}\text{ }\text{m/s}\) in uniform magnetic and electric fields, which are perpendicular to each other. If the electric field is switched off, the proton moves in a circular path of radius \(1.6\times 1{0}^{−5}\text{ }\text{m}\). The magnetic field (\(B\)) is:

(Shift II Memory Based)

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

[JEE Main 2025, 24 Jan (Shift 2)]

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 ______ .

\(\left({\mu }_{o}=4\pi \times {10}^{-7}Tm/A,\pi =3.14\right)\)

[JEE Main 2026, 6 Apr (Shift 1)]

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

[JEE Main 2025, 22 Jan (Shift 2)]

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 ____ μT. \(\left(\frac{{\mu }_{0}}{4\pi }={10}^{-7}N/{A}^{2}\right)\)

[JEE Main 2026, 6 Apr (Shift 2)]

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

[JEE Main 2026, 8 Apr (Shift 2)]

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

[02 April, 2026 (Shift-2)]

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be

A proton is moving with a uniform velocity of \(2\times 1{0}^{8}\text{ }\text{m/s}\) in uniform magnetic and electric fields, which are perpendicular to each other. If the electric field is switched off, the proton moves in a circular path of radius \(1.6\times 1{0}^{−5}\text{ }\text{m}\). The magnetic field (\(B\)) is:

(Shift II Memory Based)

A particle of charge q and mass m is projected from origin with an initial velocity \(\vec{v}=\left(\frac{{v}_{0}}{\sqrt{2}}x+\frac{{v}_{0}}{\sqrt{2}}y\right).\) . There exists a uniform magnetic field \(\vec{B}={B}_{0}\hat{z}\) and a space varying electric field \(\vec{E}={E}_{\mathrm{o}}{\mathrm{e}}^{-\lambda x}\hat{x}\) within the region \(0⩽x⩽L\) After travelling a distance such that x-coordinate has changed from x = 0 to x = L, the change in the kinetic energy is______ .

[JEE Main 2026, 5 Apr (Shift 2)]

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 \({r}_{2}=6cm\). If 20 mA current flows in it then the magentic moment will be \(\alpha \times {10}^{-2}A.{m}^{2}\). The value of \(\alpha\) is_____.

[04 April, 2026 (Shift-I)]

A proton and a deuteron \((q=+ e , m=2.0 u )\) 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 deuteron path to the radius \(r_p\) of the proton path is :

A current of \(200\mu A\) deflects the coil of a moving coil galvanometer through \(60^\circ\). The current to cause deflection through \(\frac{\pi }{10}\) radian is :

[JEE Main 2024, 27 Jan (Shift 2)]

A current of \(200\mu A\) deflects the coil of a moving coil galvanometer through \(60^\circ\). The current to cause deflection through \(\frac{\pi }{10}\) radian is :

[JEE Main 2024, 27 Jan (Shift 2)]

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 :

[JEE Main 2024, 27 Jan (Shift 1)]

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 :

[JEE Main 2024, 27 Jan (Shift 1)]

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

[JEE Main 2025, 22 Jan (Shift 2)]

An equilateral triangle frame of side \(l\) is carrying current \(i\), find magnetic field at its centroid

(Shift - II Memory Based)

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 :

[JEE Main 2025, 24 Jan (Shift 2)]

In a moving coil galvanometer, two moving coils \({\mathrm{M}}_{1}\) and \({\mathrm{M}}_{2}\) have the following particulars :

\({\mathrm{R}}_{1}=5\Omega ,{\mathrm{N}}_{1}=15,{\mathrm{A}}_{1}=3.6\times {10}^{-3}{\mathrm{m}}^{2},\)\({\mathrm{B}}_{1}=0.25\mathrm{T}\)
\({\mathrm{R}}_{2}=7\Omega ,{\mathrm{N}}_{2}=21,{\mathrm{A}}_{2}=1.8\times {10}^{-3}{\mathrm{m}}^{2},\)\({\mathrm{B}}_{2}=0.50\mathrm{T}\)
Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of \({\mathrm{M}}_{1}\) and \({\mathrm{M}}_{2}\)?

[JEE Main 2025, 2 Apr (Shift 2)]

Let \({B}_{1}\) be the magnitude of magnetic field at center of a circular coil of radius R carrying current I . Let \({\mathrm{B}}_{2}\) be the magnitude of magnetic field at an axial distance ' x ' from the center. For \(\mathrm{x}:\mathrm{R}=3:4,\frac{{\mathrm{B}}_{2}}{{\mathrm{B}}_{1}}\) is :

[JEE Main 2025, 2 Apr (Shift 1)]

A solenoid has a core made of material with relative permeability 400. The magnetic field produced in the interior of solenoid is 1.0 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.)

[JEE Main 2026, 4 Apr (Shift 2)]

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be

[JEE Main 2025, 29 Jan (Shift 1)]

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be

[JEE Main 2025, 29 Jan (Shift 1)]

An equilateral triangle frame of side \(l\) is carrying current \(i\), find magnetic field at its centroid

(Shift - II Memory Based)

A galvanmeter has a coil of resistance \(200\Omega\) with a full scale deflection at \(20\mu \mathrm{A}\). The value of resistance to be added to use it as an ammeter of range \((0-20)\mathrm{mA}\) is :

[JEE Main 2024, 09 Apr (Shift 1)]

A galvanmeter has a coil of resistance \(200\Omega\) with a full scale deflection at \(20\mu \mathrm{A}\). The value of resistance to be added to use it as an ammeter of range \((0-20)\mathrm{mA}\) is :

[JEE Main 2024, 09 Apr (Shift 1)]

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If oxygen ion \(\left({\mathrm{O}}^{-2}\right)\) and Hydrogen ion \(\left({\mathrm{H}}^{+}\right)\)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 statement, choose the correct answer from the options given below

[JEE Main 2025, 3 Apr (Shift 2)]

A circular current loop of radius R is placed inside square loop of side length \(L(L≫R)\)such that they are co-planar and their centers coincide. The permeability of free space is \({\mu }_{0}\). The mutual inductance between circular loop and square loop is _______.

[02 April, 2026 (Shift-2)]

Let \({B}_{1}\) be the magnitude of magnetic field at center of a circular coil of radius R carrying current I . Let \({\mathrm{B}}_{2}\) be the magnitude of magnetic field at an axial distance ' x ' from the center. For \(\mathrm{x}:\mathrm{R}=3:4,\frac{{\mathrm{B}}_{2}}{{\mathrm{B}}_{1}}\) is :

[JEE Main 2025, 2 Apr (Shift 1)]

For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is 2 div/mA will be:

[JEE Main 2021, 27 Aug (Shift 2)]

A solenoid of 1000 turns per metre has a core with relative permeability 500 . Insulated windings of the solenoid carry an electric current of \(5\mathrm{A}\). The magnetic flux density produced by the solenoid is:(Permeability of free space is \(4\pi \times {10}^{-7}\))

[JEE Main 2021, 17 Mar (Shift 1)]

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let \(r_d\) and \(r_\alpha\) be their respective radii of circular path. The value \(\frac{r_d}{r_\alpha}\) is equal to:

An electron is moving along the positive \(x\)-axis. If the uniform magnetic field is applied parallel to the negative \(z\)-axis. Then
(A) The electron will experience magnetic force along positive \(y\)-axis
(B) The electron will experience magnetic force along negative \(y\)-axis.
(C) The electron will not experience any force in magnetic field
(D) The electron will continue to move along the positive \(x\)-axis
(E) The electron will move along circular path in magnetic field
Choose the correct answer from the options given below :

[JEE Main 2023, 13 Apr (Shift 2)]

Two long straight wires P and Q carrying equal current of 10A each were kept parallel to each other at a distance of 5cm. Magnitude of magnetic force experienced by 10 cm length of wire P is \({F}_{1}\). If distance between the wires is halved and currents on them are doubled, force \({F}_{2}\) on 10 cm length of wire P will be:

[JEE Main 2023, 24 Jan (Shift 1)]

A charged particle carrying charge \(1 \mu \mathrm{C}\) is moving with velocity \((2 \hat{i}+3 \hat{j}+4 \hat{k}) \mathrm{ms}^{-1}\). If an external magnetic field \((5 \hat{i}+3 \hat{j}-6 \hat{k}) \times 10^{-3} T\) exists in the region where the particle is moving then the force on the particle is \(\vec{F} \times 10^{-9} N\). The vector \(\vec{F}\) is:

For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10mA is passed through it. If the torsional constant of the suspension wire is \(4.0\times {10}^{-5}\)Nm rad^–1, the magnetic field is 0.01T and the number of turns in the coil is 200, the area of each turn (in \(c{m}^{2}\) ) is:

Two ions of masses 4 amu and 16 amu have charges +2 e and +3 e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then:

[JEE Main 2023, 8 Apr (Shift 2)]

A long solenoid is formed by winding 70 turns \(\mathrm{cm}^{-1}\). If \(2.0 \mathrm{~A}\) current flows, then the magnetic field produced inside the solenoid is \(\left(\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right)\)

The current sensitivity of moving coil galvanometer is increased by 25%. This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be:

[JEE Main 2023, 11 Apr (Shift 1)]

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2A flows through it is:

[JEE Main 2023, 25 Jan (Shift 1)]

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:

[JEE Main 2023, 29 Jan (Shift 2)]

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.
A. The electron will experience magnetic force along the axis of the solenoid.
B. The electron will not experience magnetic force.
C. The electron will continue to move along the axis of the solenoid.
D. The electron will be accelerated along the axis of the solenoid.
E. The electron will follow parabolic path-inside the solenoid.

Choose the correct answer from the options given below:

[JEE Main 2024, 30 Jan (Shift 1)]

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

[JEE Main 2023, 31 Jan (Shift 2)]

Given below are two statement:
Statement-I : If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.

Statement-II : Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio:

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

[JEE Main 2023, 10 Apr (Shift 1)]

The magnetic moments associated with two closely wound circular coils A and B of radius \({r}_{A}=10cm\) and \({r}_{B}=20cm\) respectively are equal if: (Where \({N}_{A},{I}_{A}\) and \({N}_{B},{I}_{B}\) are number of turn and current of A and B respectively)

[JEE Main 2023, 30 Jan (Shift 1)]

A charged particle carrying charge \(1 \mu \mathrm{C}\) is moving with velocity \((2 \hat{i}+3 \hat{j}+4 \hat{k}) \mathrm{ms}^{-1}\). If an external magnetic field \((5 \hat{i}+3 \hat{j}-6 \hat{k}) \times 10^{-3} T\) exists in the region where the particle is moving then the force on the particle is \(\vec{F} \times 10^{-9} N\). The vector \(\vec{F}\) is:

[JEE Main 2023, 10 Apr (Shift 2)]

A wire of length \( \mathrm{L} \) metre carrying a current of I ampere is bent in the form of a circle. its magnetic moment is.

[Re-NEET 2020]

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

[JEE Main 2023, 24 Jan (Shift 1)]

A beam of protons with speed \(4 \times 10^5 \mathrm{~ms}^{-1}\) enters a uniform magnetic field of \(0.3 \mathrm{~T}\) at an angle of \(60^{\circ}\) to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton = \(1.67 \times 10^{-27} \mathrm{~kg}\), charge of the proton \(=1.69 \times 10^{-19} \mathrm{C}\) )

[JEE mains 2020]

A rod with circular cross-section area \(2c{m}^{2}\) and length 40cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4A flows in the wire windings, the total magnetic flux produced inside windings is \(4\pi \times {10}^{-6}Wb\). The relative permeability of the rod is
(Given: Permeability of vacuum \({\mu }_{0}=4\pi \times {10}^{-7}N{A}^{-2}\) )

[JEE Main 2023, 31 Jan (Shift 1)]

A charge Q is moving \(d\vec{ℓ}\) distance in the magnetic field \(\vec{B}\). Find the value of work done by \(\vec{B}\).

[JEE Main 2021, 16 Mar (Shift 2)]

Two ions of masses 4 amu and 16 amu have charges +2 e and +3 e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then:

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let \({r}_{d}\) and \({r}_{\alpha }\) be their respective radii of circular path. The value of \(\frac{{r}_{d}}{{r}_{\alpha }}\) is equal to :

[JEE Main 2021, 20 Jul (Shift 1)]

Two long straight wires \(P\) and \(Q\) carrying equal current of \(10 A\) each were kept parallel to each other at a distance of \(5 cm\). Magnitude of magnetic force experienced by \(10 cm\) length of wire \(P\) is \(F_1\). If distance between the wires is halved and currents on them are doubled, force \(F_2\) on 10 cm length of wire \(P\) will be:

[JEE Main 2023, 24 Jan (Shift 1)]

Magnetic fields at two points on the axis of a circular coil at a distance of \(\ 0.05 \mathrm{~m} \) and 0.2 \(\ \mathrm{m} \) from the centre are in the ratio \(\ 8: 1\). The radius of coil is:

[JEE Main 2021, 25 Feb (Shift 1)]

An electron is moving along the positive x-axis. If the uniform magnetic field is applied parallel to the negative z-axis. then,
A. The electron will experience magnetic force along positive y-axis.

B. The electron will experience magnetic force along negative y-axis.

C. The electron will not experience any force in magnetic field

D. The electron will continue to move along the positive x-axis.

E. The electron will move along circular path in magnetic field

Choose the correct answer from the options given below:

[JEE Main 2023, 13 Apr (Shift 2)]

The magnetic field vector of an electromagnetic wave is given by \(B={B}_{0}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\cos (kz-\omega t)\) where \(\hat{i},\hat{j}\) represents unit vector along x and y-axis respectively. At t = 0s, two electric charges \({q}_{1}\) of \(4\pi\) coulomb and \({q}_{2}\) of \(2\pi\) coulomb located at \(\left(0,0,\frac{\pi }{k}\right)\) and \(\left(0,0,\frac{3\pi }{k}\right)\) respectively, have the same velocity of \(0.5c\hat{i}\) (where c is the velocity of light). The ratio of the force acting on charge \({q}_{1}\) to \({q}_{2}\) is:

[JEE Main 2021, 26 Aug (Shift 2)]