1. OBJECTIVE UNSOLVED LEVEL - I
1. A coil having N turns is wound tightly in the formof a spiral with inner and outer radii a and b
respectively. Whena current I passes through the coil, the magnetic field at the centre is.
(a)
b
NI
μ0
(b)
a
NI
μ
2 0
(c)   a
b
ln
a
b
2
NI
μ0

(d)  
0
ln .
IN b
b a a


A
B
2. Two particles A and B of masses mA
and mB
respectively and having the same
charge are moving in a plane. A uniform magnetic field exists perpendicular to
this plane. The speeds of the particles are vA
and vB
respectively and the
trajectories are as shown in the figure then
(a) mA
vA
< mB
vB
(b) mA
vA
> mB
vB
(c) mA
< mB
and vA
< vB
(d) mA
= mB
and vA
= vB
.
3. An ionized gas contains both positive and negative ions. Ifit is subjected simultaneouslyto an
electric field alongthe +x directionand a magnetic field along the+z direction, then
(a) positive ionsdeflect towards +ydirectionand negative ions towards -ydirection
(b) allions deflect towards +ydirection
(c) allions deflect towards -ydirection
(d) positive ionsdeflect towards -ydirectionand negative ions towards+ydirection.
M
R
S
I
P 900
900
Q
-
- +
4. An infinitely long conductor PQR is bent to form a right angle as
shown. A current I flows through PQR. The magnetic field due to
this current at thepoint M is H1
. Now another infinitely long straight
conductor QS is connected at Q so that the current is I/2 in QR as
well as in QS, the current in PQ remaining unchanged. The mag-
netic field at M is now H2
. The ratio H1
/H2
is given by:
(a) 1/2 (b) 1
(c) 2/3 (d) 2.
5. A circular loop of radius R, carrying current I, lies in xyplane with its centre at origin. The total
magnetic fluxthroughxyplaneis:
(a) directlyproportionalto I (b) directlyproportionalto R
(c) inverselyproportionalto R (d) zero.
6. A particle is moves in acircular path ofdiameter 1.0 munder theaction ofmagnetic field of0.40
Tesla.Anelectric field of200V/mmakes the pathofparticle straight. Find the charge / mass ratio
ofthe particle
(a) 5
2.5 10 /kg
C
 (b) 5
2 10 /kg
C

(c) 5
3.5 10 /kg
C
 (d) 5
3 10 /kg
C
 .

2. 7. A charged particle is released fromrest in a regionof steady and uniformelectric and magnetic
fields whichare parallelto eachother. The particle willmove in a
(a) straight line (b) circle
(c) helix (d) cycloid.
8. A proton, a deutron and an α -particle having the same kinetic energy are moving in circular
trajectories in a constant magnetic field. IfrP
, rd
and rα denoterespectivelythe radiiofthe trajec-
tories ofthese particles then
(a) d
p
α r
r
r 
 (b) p
d
α r
r
r 

(c) p
d
α r
r
r 
 (d) α
d
p r
r
r 
 .
9. Two thin long parallel wires separated by a distance b are carrying a current i amp. each. The
magnitude oftheforce per unit lengthexerted byone wire onthe other is
(a) 2
2
0
b
μ i
(b)
b
π
2
μ 2
0i
(c)
b
π
2
μ0i
(d) 2
0
b
π
μ i
.
10. A charged particle ofmass mand charge q enters amagnetic field B witha velocity v at an angle
θ withthe direction ofB. Theradius ofthe resultingpath is
(a) B
θ
sin
q
mv
(b) θ
sin
B
q
mv
(c) B
q
mv
(d) B
θ
tan
q
mv
.
11. Anelectronfallingfreelyundergravityentersaregionofuniformhorizontalmagnetic fieldpointing
north to south. The particle willbe deflected towards
(a) east (b) west
(c) north (d) south.
12. A uniform magnetic field of magnitude 0.20 T exists in space from east to west. With what speed
should a particle of mass 0.010 g and having a charge 5
1.0 10 C

 be projected from south to north
so that it moves with a uniform velocity
(a) 48 m/s (b) 49 m/s
(c) 47 m/s (d) 50 m/s
13. In a region of space uniform electric field is present as j
ˆ
E
E 0
 and uniform magnetic field is
present as k̂
.
B
B 0
 . An electron is released from rest at origin. Which of the following best
represents the path followed by electron after release.

3. x
y
(a)
x
y
(b)
x
y
(c) (d)
Z
y
A
14. The negatively charged disc in figure is rotated clock-wise. What is
the direction of the magnetic field at point A in the plane of the
disc?
(a) Into the page (b) Out of the page
(c) Up the page (d) Down the page.
15. Which of the following particle will have minimum frequency of revolution when projected with the
same velocity perpendicular to a magnetic field?
(a) electron (b) proton
(c) He+
(d) Li+
.

4. OBJECTIVE UNSOLVED LEVEL - II
1. Aparticle ofmass mand chargeq moves withaconstant velocityvalongthe positive x-direction.
It enters a region containing a uniformmagnetic field B directed along the negative z direction,
extending fromx= a to x= b. The minimumvalue ofv required so that the particle can just enter
the region x> b is
(a) qb B/m (b) q (b-a)B/m
(c) qa B/m (d) q(b+a) B/2m.
2. Along straight wire along the z-axiscarries a current Iinthe negative zdirection. The magnetic
vector field B at a point having coordintes (x, y) in the z = 0 plane is:
(a)
0
2 2
ˆ ˆ
I(yi xj)
2 (x y )
 
 
(b)
0
2 2
ˆ ˆ
I(yi xj)
2 (x y )
 
 
(c)
0
2 2
ˆ ˆ
I(xj yi)
2 (x y )
 
 
(d)
0
2 2
ˆ ˆ
I(xj yi)
2 (x y )
 
 
.
x
y
z
2a
3. A non-planar loop of conducting wire carrying a current I is placed
as shown in the figure. Each of the straight sections of the loop is of
length 2a. The magnetic filed due to this loop at the point P (a, 0, a)
points in the direction.
(a)
1 ˆ ˆ
( j k)
2
  (b)
1 ˆ ˆ ˆ
( j k i)
3
  
(c)
1 ˆ ˆ ˆ
(i j k)
3
  (d)
1 ˆ ˆ
(i k)
2
 .
4. A long, straight wire carries a current along the Z-axis. One can find two points in the X-Y plane such
that
(a) the magnetic fields are equal
(b) the directions of the magnetic fields are the same
(c) the magnitudes of the magnetic fields are equal
(d) the field at one point is opposite to that at the other point.
5. In a coaxial, straight cable, the central conductor and the outer conductor carrry equal currents in
opposite directions. The magnetic field is zero.
(a) outside the cable (b) inside the inner conductor
(c) inside the outer conductor (d) in between the two conductors.
6. Two parallel, long wires carry currents i1
and i2
with i1
> i2
. When the currents are in the same
direction, the magnetic field at a point midway between the wires is 90 T
 . If the direction of is
reversed, the field becomes 30 T
 . The ratio 1 2
i /i is
(a) 4 (b) 3
(c) 2 (d) 1.

5. 7. Two long parallelwires are at a distane 2d apart. Theycarrysteadyequalcurrents flowing out of
the plane ofthe paper, as shown. The variationofthe magnetic field B alongthe line XX' is given
by:
(a)
x '
x
B
d d
(b)
x '
x
B
d d
(c)
x '
x
B
d d
(d)
x '
x
d d
.
8. Two insulated rings, one of slightly smaller diameter than the other,
are suspended along their common diameter as shown. Initially the
planes of the rings are mutually perpendicular. When a steady cur-
rent is set up in each of them.
(a) the two rings rotate into acommonplane
(b) the innerring oscillatesabout itsinitialposition
(c) the outerring stays stationarywhile the inner one moves into the plane ofthe outer ring
(d) the innerring stays stationarywhile the outer one moves into the plane ofthe inner ring.
9. A charged particle goes undeflected in a region containing electric and magnetic field. It is possible
that
(a) E||B, v || E
  

(b) E

is not parallel to B

(c) v||B


but E

is not parallel to B

(d) E || B
 
but v

is not parallel to E

.
10. A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the
path described by the particle is proportional to
(a) the velocity (b) the momentum
(c) the kinetic energy (d) none of these.
11. The magnetic field at the origin due to a current element idl

placed at a position r

is
(a) 0
3
i d r
4 r
l
 

 
(b) 0
3
i r d
4 r
l
 




(c) 0
3
i r d
4 r
l
 



(d) 0
3
i d r
4 r
l
 


 
.

6. 12. A proton of mass 1.67 × 10-27
kg and charge 1.6 × 10-19
C is projected with a speed of 2 × 106
m/s at an angle of 600
to the X-axis in XY plane. If a uniform magnetic field of 0.104 tesla is
applied along the Y-axis, the path ofthe proton is
(a) a circle of radius  0.1 mand time period 7
10 s


(b) a circle of radius  0.2 mand time period s
10
π 7


(c) a helix ofradius  0.1 mand time period s
10
π
2 7


(d) a helix ofradius  0.2 mand time period s
10
π
4 7

 .
13. Apotential difference of 500 V is applied across a parallel plate capacitor. The separation be-
tween the plates is 2×10-3
m. The plates of the capacitor are vertical. An electron is projected
verticallyupwards betweenthe plateswitha velocityof105
m/sand it movesundeflected between
the plates. The magnetic field acting perpendicular to the electric fieldhas magnitude of
(a) 0 Wb/m2
(b) 2.5 Wb/m2
(c) 3.0 Wb/m2
(d) 5.0 Wb/m2
.
14. Two similar coaxial coils, separated bysome distance, carrythe same current I but in opposite
directions. The magnitude ofthe magneticfield B at apoint onthe axis at the mid point ofthe line
joining the centre is :
(a) zero
(b) the same as that produced byone coil
(c) twice that produced byone coil
(d) halfofthat produced byone coil.
O
Y
C
R
R
B
R
X
I
I
A
R
15. Conductor ABC consist of two quarter circular path of radius R
lies in X-Y plane and carries current I as shown. A uniform mag-
netic field B

is switched on in the region that exert force
F

= 2 IRB0 k̂ on conductor ABC. B

can be
(a) )
î
(
B

2
0
(b)
0 ˆ
2
B
i
(c) )
ĵ
î
(
2
B0
 (d) both (b) and (c).