1
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2 Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I1 in the anti-clockwise direction and the larger loop carries current I2 in the clockwise direction, with I2 > 2I1. $$\overrightarrow B$$(x, y) denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) correct? A
$$\overrightarrow B$$(x, y) is perpendicular to the xy-plane at any point in the plane
B
| $$\overrightarrow B$$(x, y) | depends on x and y only through the radial distance $$r = \sqrt {{x^2} + {y^2}}$$
C
| $$\overrightarrow B$$(x, y) | is non-zero at all points for r < R
D
$$\overrightarrow B$$(x, y) points normally outward from the xy-plane for all the points between the two loops
2
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2 A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at the distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure).

A resistor R = 1.4 $$\Omega$$ and a capacitor C0 = 5.0$$\mu$$F are connected in series between the rails. At time t = 0, C0 is uncharged. Which of the following statement(s) is(are) correct? [$$\mu$$0 = 4$$\pi$$ $$\times$$ 10$$-$$7 SI units. Take ln 2 = 0.7] A
Maximum current through R is 1.2 $$\times$$ 10$$-$$6 ampere
B
Maximum current through R is 3.8 $$\times$$ 10$$-$$6 ampere
C
Maximum charge on capacitor C0 is 8.4 $$\times$$ 10$$-$$12 coulomb
D
Maximum charge on capacitor C0 is 2.4 $$\times$$ 10$$-$$12 coulomb
3
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Two infinitely long straight wires lie in the $$xy$$-plane along the lines $$x = \pm R.$$ The wire located at $$x = + R$$ carries a constant current $${I_1}$$ and the wire located at $$x=-R$$ carries a constant current $${I_2}.$$ A circular loop of radius $$R$$ is suspended with its center at $$\left( {0,0,\sqrt 3 R} \right)$$ and in a plane parallel to the $$xy$$-plane. This loop carries a constant current $$I$$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $$+ \widehat j$$ direction. which of the following statements regarding the magnetic field $$\overrightarrow B$$ is (are) true?
A
If $${I_1} = {I_2},$$ then $$\overrightarrow B$$ cannot be equal to zero at the origin $$(0,0,0)$$
B
If $${I_1} > 0$$ and $${I_2} < 0,$$ then $$\overrightarrow B$$ can be equal to zero at the origin $$(0,0,0)$$
C
If $${I_1} < 0$$ and $${I_2} > 0,$$ then $$\overrightarrow B$$ can be equal to zero at the origin $$(0,0,0)$$
D
If $${I_1} = {I_2},$$ then the $$z$$-component of the magnetic field at the center of the loop is $$\left( { - {{{\mu _0}I} \over {2R}}} \right)$$
4
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
A uniform magnetic field $$B$$ exist in the region between $$x=0$$ and $$x = {{3R} \over 2}$$ (region $$2$$ in the figure) pointing normally into the plane of the paper. A particle with charge $$+Q$$ and momentum $$p$$ directed along $$x$$-axis enters region $$2$$ from region $$1$$\$ at point $${P_1}\left( y \right) = - R).$$ Which of the following option(s) is/are correct? A
For $$B > {2 \over 3}{p \over {QR}}$$ the particle well re-enter region $$1$$
B
For $$B = {8 \over {13}}{p \over {QR}},$$ the particle will enter region $$3$$ through the point $${P_2}$$ on $$x$$-axis
C
When the particle re-enters region $$1$$ through the longest possible path in region $$2,$$ the magnitude of the change in its linear momentum between point $${P_1}$$ and the farthest point from $$y$$-axis is $$p/\sqrt 2$$
D
For a fixed $$B,$$ particles of same charge $$Q$$ and same velocity $$v,$$ the distance between the point $${P_1}$$ and the point of re-entry into region $$1$$ is inversely proportional to the mass of the particle
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