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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2002

MCQ (Single Correct Answer)
Wires $$1$$ and $$2$$ carrying currents $$i{}_1$$ and $$i{}_2$$ respectively are inclined at an angle $$\theta $$ to each other. What is the force on a small element $$dl$$ of wire $$2$$ at a distance of $$r$$ from wire $$1$$ (as shown in figure) due to the magnetic field of wire $$1$$?
A
$${{{\mu _0}} \over {2\pi r}}{i_1}{i_2}\,dl\,\tan \,\theta $$
B
$${{{\mu _0}} \over {2\pi r}}{i_1}{i_2}\,dl\,\sin \,\theta $$
C
$${{{\mu _0}} \over {2\pi r}}{i_1}{i_2}\,dl\,\cos \,\theta $$
D
$${{{\mu _0}} \over {4\pi r}}{i_1}{i_2}\,dl\,\sin \,\theta $$

Explanation

Magnetic field due to current in wire $$1$$ at point $$P$$ distant $$r$$ from the wire is



$$B = {{{\mu _0}} \over {4\pi }}{{{i_1}} \over r}\left[ {\cos \theta + \cos \theta } \right]$$

$$B = {{{\mu _0}} \over {2\pi }}{{{i_1}\cos \theta } \over r}$$ (directed perpendicular to the plane of paper, inwards)

The force exerted due to this magnetic field on current element $${i_2}\,dl$$ is

$$dF = {i_2}\,dl\,B\,\sin \,{90^ \circ }$$

$$\therefore$$ $$dF = {i_2}dl\left[ {{{{\mu _0}} \over {2\pi }}{{{i_1}\cos \theta } \over r}} \right]$$

$$ = {{{\mu _0}} \over {2\pi r}}{i_1}\,{i_2}dl\,\cos \,\theta $$
2

AIEEE 2002

MCQ (Single Correct Answer)
The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its
A
speed
B
mass
C
charge
D
magnetic induction

Explanation

KEY CONCEPT : The time period of a charged particle

$$\left( {m,q} \right)$$ moving in a magnetic field $$(B)$$ is $$T = {{2\pi m} \over {qB}}$$

The time period does not depend on the speed of the particle.
3

AIEEE 2002

MCQ (Single Correct Answer)
If an electron and a proton having same momentum enter perpendicular to a magnetic field, then
A
curved path of electron and proton will be same (ignoring the sense of revolution)
B
they will move undeflected
C
curved path of electron is more curved than that of the proton
D
path of proton is more curved.

Explanation

KEY CONCEPT : When a charged particle enters perpendicular to a magnetic field,

then it moves in a circular path of radius.

$$r = {p \over {qB}}$$

where $$q=$$ Charge of the particle

$$p=$$ Momentum of the particle

$$B=$$ Magnetic field

Here $$p,q$$ and $$B$$ are constant for electron and proton, therefore the radius will be

same.
4

AIEEE 2002

MCQ (Single Correct Answer)
If in a circular coil $$A$$ of radius $$R,$$ current $$I$$ is flowing and in another coil $$B$$ of radius $$2R$$ a current $$2I$$ is flowing, then the ratio of the magnetic fields $${B_A}$$ and $${B_B}$$, produced by them will be
A
$$1$$
B
$$2$$
C
$$1/2$$
D
$$4$$

Explanation

KEY CONCEPT : We know that the magnetic field produced by a current carrying circular coil of radius $$r$$

at its center is $$B = {{{\mu _0}} \over {4\pi }}{I \over r} \times 2\pi $$

Here $${B_A} = {{{\mu _0}} \over {4\pi }}{I \over R} \times 2\pi $$ and

$${B_B} = {{{\mu _0}} \over {4\pi }}{{2I} \over {2R}} \times 2\pi $$

$$ \Rightarrow {{{B_A}} \over {B{}_B}} = 1$$

Questions Asked from Magnetics

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
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JEE Main 2020 (Online) 6th September Evening Slot (3)
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JEE Main 2019 (Online) 9th January Morning Slot (5)
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JEE Main 2018 (Online) 16th April Morning Slot (2)
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JEE Main 2018 (Offline) (2)
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AIEEE 2006 (3)
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