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*Simulator***Previous Years AIEEE/JEE Mains Questions**Q. Due to the presence of the current $\mathrm{I}_{1}$ at the origin:-
(1) The magnitude of the net force on the loop is given by $\frac{\mathrm{I}_{1} \mathrm{I}}{4 \pi} \mu_{0}\left[2(\mathrm{b}-\mathrm{a})+\frac{\pi}{3}(\mathrm{a}+\mathrm{b})\right]$
(2) The magnitude of the net force on the loop is given by $\frac{\mu_{0} \mathrm{I} \mathrm{I}_{1}}{24 \mathrm{ab}}(\mathrm{b}-\mathrm{a})$
(3) The forces on $\mathrm{AB}$ and $\mathrm{DC}$ are zero
(4) The forces on $\mathrm{AD}$ and $\mathrm{BC}$ are zero

**[AIEEE - 2009]**Ans. (4)
For AD and BC, $\overrightarrow{\mathrm{B}} \square \overrightarrow{\mathrm{dL}}$. Hence force on AD and BC is zero.

Q. Two short bar magnets of length 1 cm each have magnetic moments $1.20 \mathrm{Am}^{2}$ and $1.00 \mathrm{Am}^{2}$ 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 cm. The value of the resultant horizontal magnetic induction at the midpoint O of the line joining their centres is close to :-
(Horizontal component of earth's magnetic induction is $\left.3.6 \times 10^{-5} \mathrm{Wb} / \mathrm{m}^{2}\right)$
(1) $3.6 \times 10^{-5} \mathrm{Wb} / \mathrm{m}^{2}$
(2) $2.56 \times 10^{-4} \mathrm{Wb} / \mathrm{m}^{2}$
(3) $3.50 \times 10^{-4} \mathrm{Wb} / \mathrm{m}^{2}$
(4) $5.80 \times 10^{-4} \mathrm{Wb} / \mathrm{m}^{2}$

**[JEE(Mains) - 2013]**Ans. (2)

Q. The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times 10^{3} \mathrm{A} \mathrm{m}^{-1}$. The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetized when inside the solenoid, is :
(1) 3A (2) 6 A (3) 30 mA (4) 60 mA

**[JEE(Mains) - 2014]**Ans. (1)

Q. Hysteresis loops for two magnetic materials A and B are given below :
These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use ;
(1) B for electromagnets and transformers.
(2) A for electric generators and transformers.
(3) A for electromagnets and B for electric transformers.
(4) A for transformers and B for electric generators.

**[JEE(Mains) - 2016]**Ans. (1)
For electromagnet and transformers, we require the core that can be magnitised and demagnetised quickly when subjected to alternating current. From the given graphs, graph B is suitable.

Q. A magnetic needle of magnetic moment $6.7 \times 10^{-2} \mathrm{Am}^{2}$ and moment of inertia $7.5 \times 10^{-6} \mathrm{kg} \mathrm{m}^{2}$ is performing simple harmonic oscillations in a magnetic field of 0.01 T.
Time taken for 10 complete oscillations is :
(1) 6.98 s
(2) 8.76 s
(3) 6.65 s
(4) 8.89 s

**[JEE(Mains) - 2017]**Ans. (3)