JEE Main Magnetic Effect of Current PYQ

56. (AIEEE 2004 )

A current i ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

A. $\frac{μ_{0}}{4 π}, \frac{2 i}{r}$ tesla

B. Zero

C. Infinite

D. $\frac{2 i}{r}$ tesla

Correct Answer is Option (B)

Using Ampere's law at a distance $r$ from axis, $B$ is same from symmetry.

$\int B . d l = μ_{0} i$

i.e., $B \times 2 π r = μ_{0} i$

Here $i$ is zero, for $r < R,$ whereas $R$ is the radius

$∴$ $B = 0$

57. (AIEEE 2003 )

A particle of mass $M$ and charge $Q$ moving with velocity $\vec{v}$ describe a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B .$ The network done by the field when the particle completes one full circle is

A. $(\frac{M v^{2}}{R}) 2 π R$

B. zero

C. $B Q 2 π R$

D. $B Q 2 π R$

Correct Answer is Option (B)

The work done, $d W = F d s \cos θ$

The angle between force and displacement is $90^{\circ} .$

Therefore work done is zero.

58. (AIEEE 2003 )

A particle of charge $- 16 \times 10^{- 18}$ coulomb moving with velocity $10 m s^{- 1}$ along the $x$ -axis enters a region where a magnetic field of induction $B$ is along the $y$ -axis, and an electric field of magnitude $10^{4} V / m$ is along the negative $z$ -axis. If the charged particle continues moving along the $x$ -axis, the magnitude of $B$ is

A. $10^{3} W b / m^{2}$

B. $10^{5} W b / m^{2}$

C. $10^{16} W b / m^{2}$

D. $10^{-3} W b / m^{2}$

Correct Answer is Option ()

59. (AIEEE 2002 )

If an electron and a proton having same momentum enter perpendicular to a magnetic field, then

A. curved path electron and proton will be same(ignoring the sence of revolution)

B. they will move undeflected

C. curved path electron is more curved than that of proton

D. path of proton is more curved.

Correct Answer is Option (A)

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

then it moves in a circular path of radius.

$r = \frac{p}{q B}$

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.

60. (AIEEE 2002 )

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

Correct Answer is Option (A)

KEY CONCEPT : The time period of a charged particle

$(m, q)$ moving in a magnetic field $(B)$ is $T = \frac{2 π m}{q B}$

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