1
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is(are)

A
In the region 0 < r < R, the magnetic field is non-zero.
B
In the region R < r < 2R, the magnetic field is along the common axis.
C
In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centred on the axis.
D
In the region r > 2R, the magnetic field is non-zero.
2
JEE Advanced 2013 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

A particle of mass M and positive charge Q, moving with a constant velocity $${\overrightarrow u _1} = 4\widehat i$$ ms$$-$$1 enters a region of uniform static magnetic field, normal to the xy plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10 ms with a velocity $${\overrightarrow u _2} = 2\left( {\sqrt 3 \widehat i + \widehat j} \right)$$ ms$$-$$1. The correct statement(s) is(are)

A
The direction of the magnetic field is $$-$$z direction.
B
The direction of the magnetic field is +z direction.
C
The magnitude of the magnetic field is $${{50\pi M} \over {3Q}}$$ units.
D
The magnitude of the magnetic field is $${{100\pi M} \over {3Q}}$$ units.
3
IIT-JEE 2012 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Consider the motion of a positive point charge in a region, there are simultaneous uniform electric and magnetic fields $$\overrightarrow E = {E_0}\widehat j$$ and $$\overrightarrow B = {B_0}\widehat j$$. At time t = 0, this charge has velocity $$\overrightarrow v$$ in the xy-plane, making an angle $$\theta$$ with the x-axis. Which of the following option(s) is(are) correct for time t > 0 ?

A
If $$\theta$$ = 0$$^\circ$$, the charge moves in a circular path in the xy-plane.
B
If $$\theta$$ = 0$$^\circ$$, the charge undergoes helical motion with constant pitch along the y-axis.
C
If $$\theta$$ = 10$$^\circ$$, the charge undergoes helical motion with its pitch increasing with time, along the y-axis.
D
If $$\theta$$ = 90$$^\circ$$, the charge undergoes linear but accelerated motion along the y-axis.
4
IIT-JEE 2011 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

A
They will never come out of the magnetic field region.
B
They will come out travelling along parallel paths.
C
They will come out at the same time.
D
They will come out at different times.
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