1
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1 Find the magnetic field at the point $$\mathrm{P}$$ in figure. The curved portion is a semicircle connected to two long straight wires. A
$$\frac{\mu_{0} i}{2 r}\left(\frac{1}{2}+\frac{1}{2 \pi}\right)$$
B
$$\frac{\mu_{\mathrm{o}} i}{2 r}\left(1+\frac{2}{\pi}\right)$$
C
$$\frac{\mu_{0} \dot{i}}{2 r}\left(\frac{1}{2}+\frac{1}{\pi}\right)$$
D
$$\frac{\mu_{0} i}{2 r}\left(1+\frac{1}{\pi}\right)$$
2
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1 A long conducting wire having a current I flowing through it, is bent into a circular coil of $\mathrm{N}$ turns. Then it is bent into a circular coil of $\mathrm{n}$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is :
A
$N^{2}: n^{2}$
B
$\mathrm{N}: \mathrm{n}$
C
$\mathrm{n}: \mathrm{N}$
D
$n^{2}: N^{2}$
3
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1 A bar magnet with a magnetic moment $$5.0 \mathrm{Am}^{2}$$ is placed in parallel position relative to a magnetic field of $$0.4 \mathrm{~T}$$. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is _____________.

A
zero
B
1 J
C
2 J
D
4 J
4
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1 A rod with circular cross-section area $$2 \mathrm{~cm}^{2}$$ and length $$40 \mathrm{~cm}$$ is wound uniformly with 400 turns of an insulated wire. If a current of $$0.4 \mathrm{~A}$$ flows in the wire windings, the total magnetic flux produced inside windings is $$4 \pi \times 10^{-6} \mathrm{~Wb}$$. The relative permeability of the rod is

(Given : Permeability of vacuum $$\mu_{0}=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$$)

A
$$\frac{5}{16}$$
B
125
C
$$\frac{32}{5}$$
D
12.5
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