JEE Main Magnetism and Matter PYQ

11. (JEE Main 2021 (Online) 25th July Morning Shift )

The value of aluminium susceptibility is 2.2 $\times$ 10^{$-$ 5}. The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is $\frac{x}{10^{4}}$ . Then the value of x is _________________.

Correct answer is (22)

$B = μ . (H + I)$

$B = μ . H (1 + \frac{1}{H})$

$B = B_{0} (1 + x)$

$B - B_{0} = B_{0} x$

$\frac{B - B_{0}}{B_{0}} = x$

$\frac{B - B_{0}}{B_{0}} \times 100 = 100 x$

$= 2.2 \times 10^{- 3} = \frac{22}{10^{4}}$

12. (JEE Main 2019 (Online) 12th January Evening Slot)

A paramagnetic material has 10²⁸ atoms/m³. Its magnetic susceptibility at temperature 350 K is 2.8 $\times$ 10^–4. Its susceptibility at 300 K is :

A. 3.726 $\times$ 10^–4

B. 2.672 $\times$ 10^–4

C. 3.672 $\times$ 10^–4

D. 3.267 $\times$ 10^{$-$ 4}

Correct option is (D)

x $α$ $\frac{1}{T_{C}}$

curie law for paramagnetic substane

$\frac{x_{1}}{x_{2}}$ = $\frac{T_{C_{2}}}{T_{C_{1}}}$

$\frac{2.8 \times 10^{- 4}}{x_{2}} = \frac{300}{350}$

x₂ = $\frac{2.8 \times 350 \times 10^{- 4}}{300}$

= 3.266 $\times$ 10^{$-$ 4}

13. (JEE Main 2019 (Online) 11th January Evening Slot)

A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 $\times$ 10^–6 J/ T when a magnetic intensity of 60 $\times$ 10³ A/m is applied. Its magnetic susceptibility is

A. 3.3 $\times$ 10^–4

B. 2.3 $\times$ 10^–2

C. 4.3 $\times$ 10^–2

D. 3.3 $\times$ 10^–2

Correct option is (A)

x = $\frac{1}{H}$

I = $\frac{M a g n e t i c m o m e n t}{V o l u m e}$

I = $\frac{20 \times 10^{- 6}}{10^{- 6}}$ = 20 N/m²

x = $\frac{20}{60 \times 10^{+ 3}}$ = $\frac{1}{3} \times 10^{- 3}$

= 0.33 $\times$ 10^{$-$ 3} = 3.3 $\times$ 10^{$-$ 4}

14. (JEE Main 2019 (Online) 9th January Morning Slot)

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The corecivity of the bar magnet is :

A. 285 A/m

B. 2600 A/m

C. 520 A/m

D. 1200 A/m

Correct option is (B)

Coercivity, H = $\frac{B}{μ_{0}}$

Inside solenoid the magnetic field,

B = $μ$ ₀ni

$∴$ H = $\frac{μ_{0} n i}{μ_{0}}$

= ni

= $\frac{N}{ℓ} \times i$

= $\frac{100}{0.2} \times 5.2$

= 2600 A/m

15. (JEE Main 2014 (Offline))

The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times 10^{3} A m^{- 1} .$ The current required to be passed in a solenoid of length $10$ $c m$ and number of turns $100,$ so that the magnet gets demagnetized when inside the solenoid, is :

A. 30 mA

B. 60 mA

C. 3 A

D. 6 A

Correct option is (C)

Magnetic field in solenoid $B = μ_{0} n i$

$\Rightarrow \frac{B}{μ_{0}} = n i$

(Where $n =$ number of turns per unit length)

$\Rightarrow \frac{B}{μ_{0}} = \frac{N i}{L}$

$\Rightarrow 3 \times 10^{3} = \frac{100 i}{10 \times 10^{- 2}}$

$\Rightarrow i = 3 A$