1
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____________.

A
$${{{\mu _0}I} \over {4\pi xy}}\left[ {\sqrt {{x^2} + {y^2}} + (x + y)} \right]$$
B
$${{{\mu _0}I} \over {4\pi xy}}\left[ {\sqrt {{x^2} + {y^2}} - (x + y)} \right]$$
C
$${{{\mu _0}Ixy} \over {4\pi }}\left[ {\sqrt {{x^2} + {y^2}} - (x + y)} \right]$$
D
$${{{\mu _0}Ixy} \over {4\pi }}\left[ {\sqrt {{x^2} + {y^2}} + (x + y)} \right]$$
2
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
3
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
$${{{\mu _0}I} \over 8}\left( {{{a - b} \over {a + b}}} \right)$$
4
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of inner and outer radii 'b' and 'c' respectively. The inner wire carries an electric current i0, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance x from the axis when (i) x < a and (ii) a < x < b ?
A
$${{{x^2}} \over {{a^2}}}$$
B
$${{{a^2}} \over {{x^2}}}$$
C
$${{{x^2}} \over {{b^2} - {a^2}}}$$
D
$${{{b^2} - {a^2}} \over {{x^2}}}$$
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