1
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
$${{{\mu _0}I} \over 8}\left( {{{a - b} \over {a + b}}} \right)$$
2
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
$${{{b^2} - {a^2}} \over {{x^2}}}$$
3
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :
A
lighter ion will be deflected less than heavier ion
B
lighter ion will be deflected more than heavier ion
C
both ions will be deflected equally
D
no ion will be deflected
4
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
The fractional change in the magnetic field intensity at a distance 'r' from centre on the axis of current carrying coil of radius 'a' to the magnetic field intensity at the centre of the same coil is : (Take r < a)
A
$${3 \over 2}{{{a^2}} \over {{r^2}}}$$
B
$${2 \over 3}{{{a^2}} \over {{r^2}}}$$
C
$${2 \over 3}{{{r^2}} \over {{a^2}}}$$
D
$${3 \over 2}{{{r^2}} \over {{a^2}}}$$
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