JEE Main Magnetism and Matter PYQ

11. (JEE Main 2019 (Online) 8th April Evening Slot)

Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing, through their midpoint P, at angle q = 45° with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant ?
(d is much larger than the dimensions of the dipole) JEE Main 2019 (Online) 8th April Evening Slot Physics - Magnetic Properties of Matter Question 45 English

A. $(\frac{μ_{0}}{4 π}) \frac{2 M}{{(d / 2)}^{3}} \times q v$

B.

C. $\sqrt{2} (\frac{μ_{0}}{4 π}) \frac{M}{{(d / 2)}^{3}} \times q v$

D. 0

Correct option is (D)

${\vec{F}}_{m} = q (\vec{V} \times \vec{B})$

$\vec{B} = {\vec{B}}_{x} + {\vec{B}}_{y}$ JEE Main 2019 (Online) 8th April Evening Slot Physics - Magnetic Properties of Matter Question 45 English Explanation Since M_y = 2M_x

$\Rightarrow | {\vec{B}}_{x} | = | {\vec{B}}_{y} |$

${\vec{B}}_{n e t}$ is parallel to $\vec{V}$

$\Rightarrow$ $\vec{F} = 0$

12. (JEE Main 2019 (Online) 10th January Morning Slot)

A magnet of total magnetic moment 10^-2 $\hat{i}$ A-m² is placed in a time varying magnetic field, B $\hat{i}$ (cos $ω t$ ) where B = 1 Tesla and $ω$ = 0.125 rad/s. The work done for reversing the direction of the magnetic moment at t = 1 second, is -

A. 0.014 J

B. 0.028 J

C. 0.01 J

D. 0.007 J

Correct option is (A)

Work done, W = $(Δ \vec{μ}) . \vec{B}$

= 2 $\times$ 10^{$-$ 2} $\times$ 1 cos(0.125)

= 0.02 J

13. (JEE Main 2017 (Offline))

A magnetic needle of magnetic moment 6.7 $\times$ 10^-2 A m² and moment of inertia 7.5 $\times$ 10^-6 kg m² is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:

A. 8.76 s

B. 6.65 s

C. 8.89 s

D. 6.98 s

Correct option is (B)

Given : Magnetic moment, M = 6.7 × 10^–2 Am²

Magnetic field, B = 0.01 T

Moment of inertia, I = 7.5 × 10^–6 Kgm²

Using, T = $2 π \sqrt{\frac{I}{M B}}$

= $2 π \sqrt{\frac{7.5 \times 10^{- 6}}{6.7 \times 10^{- 2} \times 0.01}}$

= $\frac{2 π}{10} \times 1.06$ s

Time taken for 10 complete oscillations

t = 10T = 2 $π$ × 1.06

= 6.6568 $≃$ 6.65 s

14. (JEE Main 2013 (Offline))

Two short bar magnets of length $1$ $c m$ each have magnetic moments $1.20$ $A m^{2}$ and $1.00$ $A m^{2}$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $20.0$ $c m .$ The value of the resultant horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to $($ Horizontal component of earth's magnetic induction is $3.6 \times 10.5 W b / m^{2})$

A. $3.6 \times 10.5 W b / m^{2}$

B. $2.56 \times 10.4 W b / m^{2}$

C. $3.50 \times 10.4 W b / m^{2}$

D. $5.80 \times 10.4 W b / m^{2}$

Correct option is (B)

JEE Main 2013 (Offline) Physics - Magnetic Properties of Matter Question 56 English Explanation

Given: $M_{1} = 1.20 A m^{2}$ and $M_{2} = 1.00 A m^{2}$

$r = \frac{20}{2} c m = 0.1 m$

$B_{n e t} = B_{1} + B_{2} + B_{H}$

$B_{n e t} = \frac{μ_{0} (M_{1} + M_{2})}{r^{3}} + B_{H}$

$= \frac{10^{- 7} (1.2 + 1)}{{(0.1)}^{3}} + 3.6 \times 10^{- 5}$

$= 2.56 \times 10^{- 4} w b / m^{2}$

15. (AIEEE 2005)

A magnetic needle is kept in a non-uniform magnetic field. It experiences :

A. neither a force nor a torque

B. a torque but not a force

C. a force but not a torque

D. a force and a torque

Correct option is (D)

A magnetic needle kept in non uniform magnetic field experience a force and torque due to unequal forces acting on poles.