1
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

A
uniform in the region $$r < a$$ and inversely proportional to distance $$r$$ from the axis, in the region $$r > a$$
B
zero in the region $$r < a$$ and inversely proportional to $$r$$ in the region $$r > a$$
C
directly proportional to $$r$$ in the region $$r < a$$ and inversely proportional to $$r$$ in the region $$r > a$$
D
inversely proportional to $$r$$ in the region $$r < a$$ and uniform throughout in the region $$r > a$$
2
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

As shown in the figure, a long straight conductor with semicircular arc of radius $$\frac{\pi}{10}$$m is carrying current $$\mathrm{I=3A}$$. The magnitude of the magnetic field, at the center O of the arc is :

(The permeability of the vacuum $$=4\pi\times10^{-7}~\mathrm{NA}^{-2}$$)

A
$$4\mu\mathrm{T}$$
B
$$3\mu\mathrm{T}$$
C
$$6\mu\mathrm{T}$$
D
$$1\mu\mathrm{T}$$
3
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
$$\frac{\mu_{0} i}{2 r}\left(1+\frac{1}{\pi}\right)$$
4
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
$n^{2}: N^{2}$
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