1
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

As shown in the figure, a metallic rod of linear density $$0.45 \mathrm{~kg} \mathrm{~m}^{-1}$$ is lying horizontally on a smooth inclined plane which makes an angle of $$45^{\circ}$$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $$0.15 \mathrm{~T}$$ magnetic field is acting on it in the vertical upward direction, will be :

{Use $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$}

A
30 A
B
15 A
C
10 A
D
3 A
2
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

A cyclotron is used to accelerate protons. If the operating magnetic field is $$1.0 \mathrm{~T}$$ and the radius of the cyclotron 'dees' is $$60 \mathrm{~cm}$$, the kinetic energy of the accelerated protons in MeV will be :

$$[\mathrm{use} \,\,\mathrm{m}_{\mathrm{p}}=1.6 \times 10^{-27} \mathrm{~kg}, \mathrm{e}=1.6 \times 10^{-19} \,\mathrm{C}$$ ]

A
12
B
18
C
16
D
32
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

Two concentric circular loops of radii $$r_{1}=30 \mathrm{~cm}$$ and $$r_{2}=50 \mathrm{~cm}$$ are placed in $$\mathrm{X}-\mathrm{Y}$$ plane as shown in the figure. A current $$I=7 \mathrm{~A}$$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :

A
$$\frac{7}{2} \hat{k} \,\mathrm{Am}^{2}$$
B
$$-\frac{7}{2} \hat{k} \,\mathrm{Am}^{2}$$
C
$${7}\, \hat{k} \,\mathrm{Am}^{2}$$
D
$${-7}\, \hat{k} \,\mathrm{Am}^{2}$$
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

A charge particle is moving in a uniform magnetic field $$(2 \hat{i}+3 \hat{j}) \,\mathrm{T}$$. If it has an acceleration of $$(\alpha \hat{i}-4 \hat{j})\, \mathrm{m} / \mathrm{s}^{2}$$, then the value of $$\alpha$$ will be :

A
3
B
6
C
12
D
2
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