1
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle is :

(Assume that the current is flowing in the clockwise direction.)
A
3 $$\times$$ 10$$-$$7 T, outside the plane of triangle
B
$$2\sqrt 3$$ $$\times$$ 10$$-$$7 T, outside the plane of triangle
C
$$2\sqrt 3$$ $$\times$$ 10$$-$$5 T, inside the plane of triangle
D
3 $$\times$$ 10$$-$$5 T, inside the plane of triangle
2
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
The magnetic field vector of an electromagnetic wave is given by $$B = {B_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos (kz - \omega t)$$; where $$\widehat i,\widehat j$$ represents unit vector along x and y-axis respectively. At t = 0s, two electric charges q1 of 4$$\pi$$ coulomb and q2 of 2$$\pi$$ coulomb located at $$\left( {0,0,{\pi \over k}} \right)$$ and $$\left( {0,0,{{3\pi } \over k}} \right)$$, respectively, have the same velocity of 0.5 c $$\widehat i$$, (where c is the velocity of light). The ratio of the force acting on charge q1 to q2 is :-
A
$$2\sqrt 2 :1$$
B
$$1:\sqrt 2$$
C
2 : 1
D
$$\sqrt 2 :1$$
3
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
A coil is placed in a magnetic field $$\overrightarrow B$$ as shown below :

A current is induced in the coil because $$\overrightarrow B$$ is :
A
Outward and decreasing with time
B
Parallel to the plane of coil and decreasing with time
C
Outward and increasing with time
D
Parallel to the plane of coil and increasing with time
4
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:
A
$${{{\mu _0}IN} \over {2(b - a)}}{\log _e}\left( {{b \over a}} \right)$$
B
$${{{\mu _0}I} \over 8}\left[ {{{a + b} \over {a - b}}} \right]$$
C
$${{{\mu _0}I} \over {4(a - b)}}\left[ {{1 \over a} - {1 \over b}} \right]$$
D
$${{{\mu _0}I} \over 8}\left( {{{a - b} \over {a + b}}} \right)$$
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