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CBSE Questions for Class 12 Medical Physics Moving Charges And Magnetism Quiz 4 - MCQExams.com
CBSE
Class 12 Medical Physics
Moving Charges And Magnetism
Quiz 4
A north pole of strength
θ
A m, is moved around a circle or radius 10 cm which lies around a long straight conductor carrying a current of 10 A. The work done in moving it by 2 revolutions is
Report Question
0%
4
θ
μ
J
0%
25.12
θ
μ
J
0%
400
θ
μ
J
0%
0.4
θ
μ
J
A particle consisting of two electrons is moving in a magnetic field of
(
3
i
+
2
j
)
T
with a velocity
5
×
10
5
ˆ
i
m
/
s
. The magnetic force acting on the particle will be
Report Question
0%
3.2
×
10
−
13
ˆ
k
d
y
n
e
0%
3.2
×
10
13
ˆ
k
N
0%
z
e
r
o
0%
3.2
×
10
−
13
ˆ
k
N
Explanation
→
F
=
q
(
→
v
×
→
B
)
ˉ
F
=
3
⋅
2
×
10
−
19
(
5
×
10
5
ˆ
i
×
(
3
ˆ
i
+
2
ˆ
j
)
)
=
3
.
2
×
10
−
13
ˆ
k
N
A magnet of strength
μ
A m, is moved around a circle of radius 10 cm which lies around a long straight conductor carrying a current of 10 A. The work done is nearly
Report Question
0%
4
μ
J
0%
40
μ
J
0%
400
μ
J
0%
0.4
μ
J
If the distance as well as the current in each of two parallel current carrying wires is doubled, the force per unit length acting between them becomes
Report Question
0%
doubled
0%
remains same
0%
quadrupled
0%
halved
Explanation
Force per unit length
(
F
)
between two current carrying wires is
F
=
μ
o
I
1
I
2
2
A
π
N
When both
I
1
,
I
2
and
r
are doubled then
⇒
F
′
=
μ
o
(
2
I
1
)
(
2
I
2
)
2
A
(
2
π
1
)
=
2
F
Two parallel conductors carrying 5A each, repel with a force of 0.25 N
m
−
1
. The distance between them is
Report Question
0%
4
×
10
−
5
m
0%
3
×
10
−
5
m
0%
2
×
10
−
5
m
0%
1
×
10
−
5
m
Explanation
d
f
d
l
=
μ
0
i
1
i
2
2
π
r
0
⋅
25
=
2
×
10
−
7
×
5
×
5
r
r
=
2
×
10
−
5
m
Two long straight wires carry currents 5 A and 10 A in the same direction are separated by 20 cm. The force between wires is
Report Question
0%
5
×
10
−
5
N
/
m
attractive
0%
5
×
10
−
5
N
/
m
repulsive
0%
2
×
10
−
5
N
/
m
attractive
0%
2
×
10
−
5
N
/
m
repulsive
Explanation
F
=
M
o
2
A
×
i
1
i
2
R
=
2
×
10
−
7
×
5
×
10
20
×
10
−
2
=
5
×
10
−
5
N
/
M
As both currents are in same direction, force is attractive.
The magnitude of the force between a pair of conductors, each of length
110
c
m
, carrying a current of
10
A
each and separated by a distance of
10
c
m
is (
μ
0
=
4
π
×
10
−
7
H
/
m
)
Report Question
0%
55
×
10
−
5
N
0%
44
×
10
−
5
N
0%
33
×
10
−
5
N
0%
22
×
10
−
5
N
Explanation
F
=
μ
0
i
1
i
2
2
π
r
(
l
)
=
2
×
10
−
7
×
10
×
10
×
1.1
⋅
1
=
22
×
10
−
5
N
A charged particle, having charge
q
accelerated through a potential difference
V
enters a perpendicular magnetic field in which it experiences a force
F
. If
V
is increased to
5
V
,the particle will experience a force
Report Question
0%
F
0%
5
F
0%
0.2
F
0%
√
5
F
Explanation
1
2
m
v
2
=
q
V
So
v
=
√
2
q
V
m
F
1
=
q
v
B
=
q
√
2
q
V
m
B
F
2
=
q
√
2
q
×
5
V
m
B
F
2
=
√
5
F
1
A particle of charge
q
and mass
m
moving with a velocity
v
along
x
−
axis enters the region
x
>
0
with uniform magnetic field
B
along the
ˆ
k
direction. The particle will penetrate in this region in the
x
−
direction up to a distance
d
equal to
Report Question
0%
Z
e
r
o
0%
m
v
q
B
0%
2
m
v
q
B
0%
I
n
f
i
n
i
t
y
Explanation
Lorentz force
F
=
q
(
→
v
×
→
B
)
=
q
(
v
ˆ
i
×
B
ˆ
k
)
=
−
q
v
B
ˆ
j
The particle move in a circle, the plane of the circle is perpendicular to the direction of magnetic field.
Centripetal force is provided by the Lorentz force.
q
v
B
=
m
v
2
r
⇒
r
=
m
v
q
B
Two conductors each of length
12
m
lie parallel to each other in air. The centre to centre distance between the two conductors is
15
×
10
−
2
m
and the current in each conductor is
300
A
. The force in newton tending to pull the conductors together is:
Report Question
0%
14.4
N
0%
1.44
N
0%
144
N
0%
0.144
N
Explanation
F
=
μ
0
i
1
i
2
l
2
π
r
=
2
×
10
−
7
×
300
×
300
×
12
15
×
10
−
2
=
1
⋅
44
N
The force between two parallel conductors, each of length
50
c
m
and distant
20
c
m
apart is
100
N. If the current in one conductor is double that in another one then the values will respectively be(Given
μ
0
=
4
π
×
10
−
7
)
Report Question
0%
10
4
A
and
2
×
10
4
A
0%
50
A
and
100
A
0%
10
A
and
20
A
0%
5
A
and
10
A
Explanation
F
=
μ
0
i
1
i
2
l
2
π
r
100
=
2
×
10
−
7
×
2
i
×
1
×
⋅
5
⋅
2
10
8
=
i
2
i
=
10
4
A
m
p
Current in other wire
=
2
i
=
2
×
10
4
A
m
p
The force per unit length between two long straight conductors carrying currents 3 A each in the same direction and separated by a distance of 2.0 cm is :
Report Question
0%
9
×
10
−
7
N
/
m
0%
9
×
10
−
6
N
/
m
0%
9
×
10
−
5
N
/
m
0%
9
×
10
−
4
N
/
m
Explanation
The force per unit length between two long straight current carrying conductors is given by
F
=
μ
0
I
1
I
2
2
π
d
Here, current in the conductors
I
1
=
I
2
=
3
A
,
Distance between the two conductors,
d
=
2
c
m
=
0.02
m
,
So,
F
=
4
π
×
10
−
7
×
3
×
3
2
π
×
0.02
=
9
×
10
−
5
N
/
m
Magnetic induction at the centre of a circular loop of area
π
m
2
is
0.1
T
. The magnetic moment of the loop is :
(
μ
0
is permeability of air)
Report Question
0%
0.1
π
μ
0
0%
0.2
π
μ
0
0%
0.3
π
μ
0
0%
0.4
π
μ
0
Explanation
B
at centre of loop =
μ
0
i
2
r
Given area of loop is A =
π
⇒
r
=
1
m
0.1
T
=
μ
0
i
2
×
1
i
=
0.2
μ
0
Magnetic moment
=
i
×
A
=
0.2
μ
0
×
A
=
0.2
π
μ
0
A circular coil of wire of
n
turns has a radius
r
and carries a current
i
. Its magnetic dipole moment is
M
. Now the coil is unwound and again rewound into a circular coil of half the initial radius and the same current is passed through it, then the dipole moment of this new coil is :
Report Question
0%
M
2
0%
M
4
0%
M
0%
2
M
Explanation
The length of remains same
N
1
π
∗
r
=
N
2
π
∗
r
/
2
N
2
=
2
n
M
=
N
A
I
=
n
I
π
∗
r
2
M
2
=
N
2
I
∗
π
∗
(
r
/
2
)
2
=
2
n
∗
I
π
∗
(
r
2
/
4
)
M
2
M
=
1
2
M
2
=
M
2
The distance between two parallel wires carrying current of
1
A
is
1
m
. The force per unit length between the conductors is
Report Question
0%
2
×
10
7
N
m
−
1
0%
2
×
10
−
7
N
m
−
1
0%
4
×
10
7
N
m
−
1
0%
4
×
10
−
7
N
m
−
1
Explanation
F
=
μ
0
2
A
d
i
1
i
2
=
2
×
10
−
7
×
1
×
1
1
=
2
×
10
−
7
N
/
m
In an electric motor, wires carrying a current of
5
A
are placed at right angles to a magnetic field of induction
0.8
T
. If each wire has length of
20
c
m
, then the force acting on each wire is :
Report Question
0%
0.2
N
0%
0.4
N
0%
0.6
N
0%
0.8
N
Explanation
F
=
B
i
l
=
0.8
×
5
×
20
×
10
−
2
=
0.8
N
An infinite long straight wire is bent into a semicircle of radius
R
, as shown in the figure. A current
I
is sent through the conductor. The magnetic field at the centre of the semicircle is :
Report Question
0%
∞
0%
0
0%
μ
0
4
R
I
0%
μ
0
I
4
π
R
(
π
+
1
)
Explanation
Magnetic field due to straight portion of the wire
=
0
Magnetic field due to circular portion of the wire:
=
1
2
(
μ
0
I
2
R
)
=
μ
0
I
4
R
Hence the correct answer is
μ
0
I
4
R
Two long parallel copper wires carry currents of
5
A
each in the opposite direction . If the wires are separated by a distance of
0.5
m
, then the force between the two wires is
Report Question
0%
10
−
5
N
attractive
0%
10
−
5
N
repulsive
0%
2
×
10
−
6
N
attractive
0%
2
×
10
−
5
N
repulsive.
Explanation
F
=
μ
i
1
i
2
2
π
d
=
2
×
10
−
7
×
5
×
5
0.5
=
10
−
5
N
Since currents are opposite so the force is repulsive.
The magnetic field at the centre of circular loop in the circuit carrying current
I
shown in the figure is :
Report Question
0%
μ
0
4
π
2
I
r
(
1
+
π
)
0%
μ
0
4
π
2
I
r
(
π
−
1
)
0%
μ
0
4
π
2
I
r
0%
μ
0
4
π
I
r
(
π
+
1
)
Explanation
Magnetic field due to circular loop is
B
1
=
μ
0
I
2
r
=
μ
0
I
4
π
r
2
π
field due to straight wire is
B
2
=
μ
0
I
2
π
r
=
μ
0
I
4
π
r
2
∵
net field
={ B }_{ 1 }-{ B }_{ 2 }=\dfrac { { \mu }_{ 0 }I }{ 4\pi r } \quad (2\pi-2)
=\dfrac { { \mu }_{ 0 } }{ 4\pi } \times \dfrac { 2I }{ r } \quad (\pi-1)
A current carrying small loop of one turn behaves like a small magnet. If
A
be its area,
M
its magnetic moment, the current in the loop will be
Report Question
0%
\dfrac{M}{A}
0%
\dfrac{A}{M}
0%
MA
0%
A^{2}M
Explanation
Magnetic moment
M= i \times A \implies i=M/A
Two long straight parallel wires separated by a distance, carrying equal currents exert a force F per unit length on each other. If the distance of separation is doubled, and the current in each is halved, the force per unit length, between them will be :
Report Question
0%
F
0%
F/2
0%
F/4
0%
F/8
Explanation
F=\dfrac { \mu_o{ i }_{ 1 }{ i }_{ 2 } }{ 2\pi d }
by halfing each current, we get and distance is doubled, then
F=\dfrac { \mu_o\dfrac { { i }_{ 1 } }{ 2 } \quad \dfrac { { i }_{ 2 } }{ 2 } }{ 2\pi \quad (2d) } =\dfrac { 1 }{ 8 } \quad \bigg (\dfrac { \mu_o{ i }_{ 1 }{ i }_{ 2 } }{ 2\pi d } \bigg )=\dfrac { F }{ 8 }
Two identical coils carry equal currents have a common centre and their planes are at right angles to each other. The ratio of the magnitude of the resultant magnetic field at the centre and the field due to one coil is :
Report Question
0%
2 : 1
0%
1 : 2
0%
\sqrt{2}:1
0%
1:\sqrt{2}
Explanation
The magnetic field due to each coil is equal in magnitude and perpendicular to each other
Let magnetic field due to one of them be B
Then the resultant magnetic field due to 2 coil =
\sqrt{ B^{2} +B^{2}} = \sqrt{2} B
The ratio of the magnitude of the
resultant magnetic field at the centre and the field
due to one coil =
\sqrt{2} B : B = \sqrt{2} :1
Find the magnetic field due to conducting wire at point
O,
at centre of semicircle of radius
r
and carrying a current
i
as shown in the figure.
Report Question
0%
\dfrac{\mu _{0}i}{4r}
0%
\dfrac{\mu _{0}i}{4r}(1+2\pi )
0%
\dfrac{\mu _{0}i}{4r}(\pi-2 )
0%
\dfrac{\mu _{0}i}{4\pi r}(\pi+2 )
Explanation
\left | B \right |
at centre =
\left | B \right |
due to semicircle wire+
2\times
\left | B \right |
due semi infinite wire
=\dfrac{\mu _{0}i}{4r}+\dfrac{2\mu _{0}i}{4\pi r}
=\dfrac{\mu _{0}i}{4r}\times \left ( 1+\dfrac{2}{\pi } \right )
In the given figure the magnetic induction at the point O is
Report Question
0%
\displaystyle \frac{\mu _{0}I}{4\pi r}
0%
\displaystyle \frac{\mu _{0}I}{4r}+\frac{\mu _{0}I}{2\pi r}
0%
\displaystyle \frac{\mu _{0}I}{4r}+\frac{\mu _{0}I}{4\pi r}
0%
\displaystyle \frac{\mu _{0}I}{4r}-\frac{\mu _{0}I}{4\pi r}
Explanation
Magnetic field due to circular arc on its center
=
\dfrac{\mu _{0}I}{4\pi r}\times \theta
& due to infinite current carrying straight wire at a distance r from it=
\dfrac{\mu _{0}}{2\pi r}
So
\left | B \right | = \dfrac{\mu _{0}I}{4\pi r}\times \pi + \dfrac{\mu _{0}}{4\pi r}
=
\dfrac{\mu _{0}I}{4 r} + \dfrac{\mu _{0}}{4\pi r}
The magnetic field at the center of the coil of radius
r
and carrying a current
I
as shown in the figure is : (the wires crossing at
P
are insulated from each other)
Report Question
0%
\dfrac{\mu _{0}}{4\pi}\dfrac{2I}{r}(1+\pi )
0%
\dfrac{\mu _{0}}{4\pi}\dfrac{2I}{r}(\pi-1 )
0%
\dfrac{\mu _{0}}{4\pi}\dfrac{2I}{r}(\pi^{2}+1 )
0%
\dfrac{\mu _{0}}{4\pi}\dfrac{2\pi I}{r}
Explanation
Given, radius of coil
= r
, current flowing
= I
Formula used,
i) Magnetic field due to infinite length wire,
B_{01}=\dfrac { { \mu }_{ 0 }I }{ 2\pi r }
ii) Magnetic field due to circular loop,
B_{02}=\dfrac { { \mu }_{ 0 }I }{ 2r }
\therefore
Total magnetic field at 0 is,
B=B_{01}+B_{02}
=\dfrac { { \mu }_{ 0 }I }{ 2\pi r } +\dfrac { { \mu }_{ 0 }I }{ 2r }
=\dfrac { { \mu }_{ 0 }I }{ 2r } \left( \dfrac { 1+\pi }{ \pi } \right)
B=\dfrac { { \mu }_{ 0 } }{ 4\pi } \dfrac { 2I }{ r } \left( 1+\pi \right)
Two identical circular loops each of radius
r
and carrying a current
i
are arranged concentric with each other and in perpendicular planes as shown in the given figure. The magnetic field
\vec{B}
at the common center is :
Report Question
0%
\dfrac{\mu _{0}i}{2r}
0%
\dfrac{\mu _{0}i}{\sqrt{2}r}
0%
zero
0%
\dfrac{\mu _{0}i}{r}
Explanation
Given,
i) two coils (circular loop) arranged in perpendicular planes.
ii) The radius of each loop
=r
iii) The magnetic field at common centre =?
We know that,
Induced magnetic field due to current flowing in a plane are mutually perpendicular. Thus,
B_1
is perpendicular to loop 1 plane
B_2
is perpendicular to loop 2 plane
Resultant at centre,
B_r=\sqrt { { B }_{ 1 }^{ 2 }+{ B }_{ 2 }^{ 2 } }
and
B_1=\dfrac { { \mu }_{ 0 }I }{ 2r } ={ B }_{ 2 }
\therefore B_r=\sqrt { 2 } { B }_{ 1 }
=\sqrt { 2 } \dfrac { { \mu }_{ 0 }I }{ 2r }
B_r=\dfrac { { \mu }_{ 0 }I }{ \sqrt { 2r } }
The magnetic field at the centre of a circular coil of radius r is
\pi
times that due to a long straight wire at a distance r from it, for equal currents. Figure shows three cases. In all cases the circular path has radius r and straight ones are infinitely long. For same current the B field at the centre P in cases 1,2,3 has the ratio :
Report Question
0%
-\bigg ( \dfrac{\pi }{4}+\dfrac{1}{2} \bigg ):\bigg (\dfrac{\pi}{2}\bigg ):\bigg (\dfrac{3\pi}{4}-\dfrac{1}{2}\bigg )
0%
\bigg (-\dfrac{\pi}{2}+1\bigg ):\bigg (\dfrac{\pi}{2}+1\bigg ):\bigg (\dfrac{3\pi}{4}+\dfrac{1}{2}\bigg )
0%
-\dfrac{\pi}{2}:\dfrac{\pi}{2}:\dfrac{3\pi}{4}
0%
\bigg (-\dfrac{\pi}{2}-1\bigg ):\bigg (\dfrac{\pi}{2}-\dfrac{1}{4}\bigg ):\bigg (\dfrac{3\pi}{4}+\dfrac{1}{2}\bigg )
Explanation
Magnetic field in case 1 is
{ B }_1= \dfrac { { \mu }_{ 0 } I}{ 2 r } \left( \dfrac { \pi }{ 2 \times 2 \pi} +\dfrac{1}{2\pi} \right)
outside the plane of paper
Magnetic field in case 2 is
{ B }_2= \dfrac { { \mu }_{ 0 } I}{ 4\pi r }
inside the plane of paper
Magnetic field in case 3 is
{ B }_3= \dfrac { { \mu }_{ 0 } I}{ 2r } \left( \dfrac { 3\pi }{ 2 \times 2 \pi} -\dfrac{1}{2\pi} \right)
inside the plane of paper
\therefore { B }_{ 1 }:{ B }_{ 2 }:{ B }_{ 3 }
=
-\left( \dfrac { \pi }{ 4 } +\dfrac { 1 }{ 2 } \right) : \left( \dfrac { \pi }{ 2 } \right) : \left( \dfrac { 3\pi }{ 4 } -\dfrac { 1 }{ 2 } \right) \quad
The wire shown in figure carries a current of
40A
. If
r=3.14cm
the magnetic field at point p will be :
Report Question
0%
1.6\times 10^{-3}T
0%
3.2\times 10^{-3}T
0%
6\times 10^{-4}T
0%
4.8\times 10^{-3}T
Explanation
Magnetic field due to circular arc is given by,
\left | B \right |=\dfrac{\mu _{0}I }{4\pi r}\theta
=
\dfrac{\mu _{0}I\times 3\pi }{4\pi r \times 2}
=
\dfrac{3 \mu _{0}I}{8r}
=
\dfrac{3\times 4\pi \times 10^{-7}\times 40}{8\times 3.14\times 10^{-2}}
=
6\times 10^{-4}T
A charged particle, moving at right angle to a uniform magnetic field, starts moving along a circular arc of radius of curvature
r
. In the field it now penetrates a layer of lead and loses
{\dfrac{3}{4} }^{th}
of it's initial kinetic energy. The radius of curvature of it's path now will be :
Report Question
0%
4r
0%
2r
0%
\dfrac{r}{4}
0%
\dfrac{r}{2}
Explanation
Initially,
r=\dfrac{mv}{qB}
r=\dfrac{\sqrt{2K_{e}m}}{qB}
Now
{K_{e}}'=\dfrac{1}{4}K_{e}
{r}'=\dfrac{\sqrt{2\times \bigg (\dfrac{1}{4}\bigg )K_{e}m}}{qB}
=
\dfrac{r}{2}
Two particles
X
and
Y
having equal charges, after being accelerated through the same potential differences, enter in a region of uniform magnetic field and describe circular paths of radii
R_{1}
and
R_{2}
respectively. The ratio of the mass of
X
to that of
Y
is :
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0%
\bigg (\dfrac{R_{1}}{R_{2}}\bigg )^{1/2}
0%
\bigg (\dfrac{R_{1}}{R_{2}}\bigg )^{-1}
0%
\bigg (\dfrac{R_{1}}{R_{2}}\bigg )^{2}
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\bigg (\dfrac{R_{1}}{R_{2}}\bigg )
Explanation
Since the particle is accelerated through
V
volts
\because \dfrac{mv^{2}}{2}=qV
mv=\sqrt{2mqV}
R=\dfrac{mv}{qB}
So,
R_1=\dfrac{\sqrt{2m_{1}qV}}{qB}
R_2=\dfrac{\sqrt{2m_{2}qV}}{qB}
\dfrac{m_1}{m_2}=\bigg (\dfrac{R_1}{R_2}\bigg )^{2}
In the given loop the magnetic field at the centre O is :
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0%
\dfrac{\mu _{0}I}{4}\left ( \dfrac{r_{1}+r_{2}}{r_{1}r_{2}} \right )
out of the page
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\dfrac{\mu _{0}I}{4}\left ( \dfrac{r_{1}+r_{2}}{r_{1}r_{2}} \right )
into the page
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\dfrac{\mu _{0}I}{4}\left ( \dfrac{r_{1}-r_{2}}{r_{1}r_{2}} \right )
out of the page
0%
\dfrac{\mu _{0}I}{4}\left ( \dfrac{r_{1}-r_{2}}{r_{1}r_{2}} \right )
into the page
Explanation
\left | B_{1} \right |=\dfrac{\mu _{0}I}{4r_{1}}
into the plane
\left | B_{2} \right |=\dfrac{\mu _{0}I}{4r_{2}}
into the plane
Net
\left | B_{1} \right |=\dfrac{\mu _{0}I}{4}\times \left (\dfrac{r_{1}+r_{2}}{r_{1}r_{2}} \right )
into the plane
A deutron of kinetic energy
50 keV
is describing a circular orbit of radius
0.5 m
in a plane perpendicular to magnetic field
\vec{B}
. The kinetic energy of the proton that describes a circular orbit of radius
0.5 m
in the same plane with the same
\vec{B}
is :
Report Question
0%
25 keV
0%
50 keV
0%
200 keV
0%
100 keV
Explanation
Deutron is
_{1}H^{2}
r=\dfrac{mv}{qB}
r=\dfrac{\sqrt{2K.m}}{qB}
\because r_{1}=r_{2}
\dfrac{\sqrt{2\times 50\times 2}}{B}=\dfrac{\sqrt{2\times K.1}}{B}
K=100keV
A proton of energy
E
is moving along a circular path in a uniform magnetic field. If an alpha particle describes the same circular path, its energy should be :
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4E
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2E
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E
0%
0.5E
Explanation
proton
\dfrac{mv^{2}}{2}=E
r=\dfrac{mv}{qB}
=
\dfrac{\sqrt{2Em}}{qB}
for
\alpha
particle,
M=4m \ and \ Q=2q
r=\dfrac{\sqrt{2{E}'4m}}{2qB}
r=\dfrac{\sqrt{2{E}'m}}{qB}
{E}'=E
Electrons accelerated by a potential difference
V
enter a uniform magnetic field of flux density
B
at right angles to the field. They describe a circular path of radius
r
. If now
V
is doubled and
B
is also doubled, the radius of the new circular path is :
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0%
4r
0%
2r
0%
2\sqrt{2r}
0%
\dfrac{r}{\sqrt{2}}
Explanation
Radius of charged particle in magnetic field is,
r=\dfrac{mv}{qB}
\dfrac{mv^{2}}{2}=qV
mv=\sqrt{2qVm}
r=\dfrac{mv}{qB}=\dfrac{\sqrt{2qVm}}{qB}=\dfrac{1}{B}\times\bigg (\sqrt{\dfrac{2Vm}{q}}\bigg )
{r}'=\dfrac{1}{2B}\times\bigg (\sqrt{\dfrac{2\times 2Vm}{q}}\bigg )=\dfrac{r}{\sqrt{2}}
A proton moving with a velocity of
(6\hat{i} + 8\hat{j}) \times 10^{5} \ ms^{-1}
enters uniform magnetic field of induction
5 \times 10^{-3} \hat{k}T
. The magnitude of the force acting on the proton is :
(
\hat{i}, \hat{j}
and
\hat{k}
are unit vectors forming a right handed triad)
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0
0%
8\times 10^{-16}N
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3\times 10^{-16}N
0%
4\times 10^{-16}N
Explanation
Force on a charged particle in magnetic field is given by,
\bar{F}=q\left ( {\vec{V}}{}\times \vec{B}{} \right )
=
1.6\times 10^{-19}((6\hat{i}+8\hat{j})\times 5\hat{k})\times10^{5}\times 10^{-3}
=
1.6\times 10^{-19}\times 10^{-2}(-30\hat{j}+40\hat{i})
=
1.6\times 10^{-16}(-3\hat{j}+4\hat{i})
{\left | F \right |}=1.6\times 10^{-16}\sqrt{3^{2}+4^{2}}
=
1.6\times 10^{-16}\times 5 N
=
8\times 10^{-16} N
A proton, a deuteron and an
\alpha
particle are accelerated through same potential difference and then they enter in a normal uniform magnetic field, the ratio of their kinetic energies will be:
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0%
2:1:3
0%
1:1:2
0%
1:1:1
0%
1:2:4
Explanation
Kinetic energy obtained
=qV
where
q
is the charge and
V
is the potential through which the particle is accelerated.
Also, the force due to the magnetic field is perpendicular to the direction of motion. So it cant change the speed and consequentially Kinetic energy of the particles will remain same after they enter a normal magnetic field.
In the above problem,
V
is constant.
So KE
\propto q
.
The charges of the proton, deuteron and the alpha particle are in the ratio
1 : 1 : 2
So, their kinetic energies are in the ratio
1 : 1 : 2
If a particle of charge
10^{-12}C
moving along the x-axis with a velocity
10^{5}
m/s. experiences a force of
10^{-10}N
in y-direction due to magnetic field, then the minimum magnetic field is.
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6.25\times 10^{3}T
in Z direction
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10^{-15}T
in Z direction
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6.25\times 10^{-3}T
in Z direction
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10^{-3}T
in -ve Z direction
Explanation
f=qVB\sin \theta
B will be minimum when
\theta =90^{\circ}
B=\dfrac{f}{qV}
=
\dfrac{10^{-10}}{10^{-12}\times 10^{5}}
=
10^{-3}T
in Z-direction
Acceleration experienced by a particle with specific charge
1 \times10^{7} C/kg
when fired perpendicular to a magnetic field of induction
100 T
with a velocity
10^{5} ms^{-1}
is :
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0%
10^{8} ms^{-2}
0%
10^{-6} ms^{-2}
0%
10^{14} ms^{-2}
0%
10^{-8} ms^{-2}
Explanation
Specific charge
\left(\dfrac{q}{m}\right)=10^{7} C/kg
\left | B \right |=100T
f=qVB \sin \theta
q=\dfrac{f}{m}
=
\dfrac{qVB \sin \theta}{m}
=
\dfrac{10^{7}\times 10^{5}\times 100 \times \sin 90^{\circ}}{1}
=
10^{14} ms^{-2}
A proton of energy
8eV
is moving in a circular path in a uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the same path will be
Report Question
0%
4eV
0%
2eV
0%
8eV
0%
6eV
Explanation
From the formula mentioned above, momentum of particle moving in a magnetic field
mv=p=qBr
Therefore, Kinetic Energy of that particle can be written as
KE=\dfrac{p^2}{2m}=\dfrac{q^2B^2r^2}{2m}
In the same magnetic field for the same path,
KE \propto \dfrac{q^2}{m}
This ratio is same for the alpha particle and the proton. (
\dfrac{(2e)^2}{4 amu}=\dfrac{4e^2}{4 amu}=\dfrac{e^2}{amu}
; Here
amu
is the atomic mass unit)
So, in such conditions, both will have the same energy. Hence, energy of the alpha particle will be
8 eV
too.
An electron having energy
10 eV
is circulating in a path of radius
0.1m
having a magnetic field of
10^{-4}T
. The speed of the electron will be :
Report Question
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2.0\times (10^{6})ms^{-1}
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4.8\times (10^{6})ms^{-1}
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2.0\times (10^{12})ms^{-1}
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4.8\times (10^{12})ms^{-1}
Explanation
Magnetic force provides necessary centripetal force,
qVB=\dfrac{mv^{2}}{r}
qVB=\dfrac{2KE}{r}
V=\dfrac{2KE}{qBr}
=
\dfrac{2\times 10}{10^{-4}\times 0.1}
=
2.0 \times10^{6}ms^{-1}
An electron moves with a speed
2\times 10^{5}\ m/s
along the positive x-direction in the presence of a magnetic induction
\vec{B}=\hat{i}+4\hat{j}-3\hat{k}\ T
. The magnitude of the force experienced by the electron in newton is :
(charge on the electron
=1.6 \times10^{-19}C
)
Report Question
0%
1.18\times 10^{-13}
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1.28\times 10^{-13}
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1.6\times 10^{-13}
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1.72\times 10^{-13}
Explanation
Force on charge particle in magnetic field is given by,
\bar{F}=q\left ( \vec{V}\times \vec{B} \right )
V=2\times 10^5 \hat{i}
=
1.6\times 10^{-19}(V\hat{i}\times (\hat{i}+4\hat{j}-3\hat{k}))
=
1.6\times 10^{-19}(4V\hat{k}+3V\hat{j})
=
1.6\times 10^{-19}(4\hat{k}+3\hat{j})\times 2\times 10^{5}
{ |F| }=1.6\times 10^{-13}N
Two particles having same charge and
KE
enter at right angles into the same magnetic field and travel in circular paths of radii
2 cm
and
3 cm
respectively. The ratio of their masses is :
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2 : 3
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3 : 2
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4 : 9
0%
9 : 4
Explanation
Radius of charged particle in magnetic field is,
r=\dfrac{mv}{qB}
\dfrac{mv^{2}}{2}=K_{e}
r=\dfrac{\sqrt{2K_{e}m}}{qB}
r_{1}=\dfrac{\sqrt{2K_{e}m_{1}}}{qB}
r_{2}=\dfrac{\sqrt{2K_{e}m_{2}}}{qB}
\dfrac{4}{9}=\dfrac{m_{1}}{m_{2}}
A proton of energy
2 MeV
is moving perpendicular to uniform magnetic field of
2.5 T
. The force on the proton is : (
M_p=1.6\times 10^{-27}kg
and
q_{p}=e=1.6\times 10^{-19}C
)
Report Question
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2.5\times 10^{-16}N
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8\times 10^{-11}N
0%
2.5\times 10^{-11}N
0%
8\times 10^{-12}N
Explanation
F=qvB
\dfrac{mv^{2}}{2}=K_{e}
v=\sqrt{\dfrac{2K_{e}}{m}}
\therefore f=q\times \sqrt{\dfrac{2K_{e}}{m}}\times B
=
1.6\times 10^{-19}\times \sqrt{\dfrac{2\times 2\times 10^{6}\times 1.6\times 10^{-19}}{1.6\times 10^{-27}}}\times 2.5
=
8\times 10^{-12} N
A horizontal wire carries 200 amp current below which another wire of linear density
20\times 10^{-3}kgm^{-1}
carrying a current is kept at 2 cm distance. If the wire kept below hangs in air. The current in this wire is :
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100A
0%
9.8 A
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98 A
0%
48A
Explanation
Since wire hangs in the air, So
mg=Bil
\dfrac{m}{l}=\dfrac{Bi}{g}
20\times 10^{-3}=\bigg (\dfrac{\mu _{0}i}{g2\pi r}\bigg )i
i=98A
An electron travelling with a velocity
\bar{V}=10^{7}i\ m/s
enter a magnetic field of induction
\bar{B}=\overline{2j}
. The force on electron is
Report Question
0%
1.6\times 10^{-12}\bar{j}N
0%
3.2\times 10^{-12}\bar{k}N
0%
6.4\times 10^{-12}\bar{k}N
0%
-3.2\times 10^{-12}\bar{k}N
Explanation
\bar{F}=q\left ( \underset{V}{\rightarrow}\times \underset{B}{\rightarrow} \right )
=
q\times 10^{7}\times 2\times \bar{k}
=
1.6\times 10^{-19}\times 2\times 10^{7} \bar{k} N
=
3.2\times 10^{-12}\bar{k} N
Two long parallel conductors are placed at right angles to a metre scale at the
2 cm
and
4 cm
marks, as shown in the figure. They carry currents of
1 A
and
3 A
respectively. They will produce zero magnetic field
at the
(ignore the Earth's magnetic field)
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0.5 cm
mark
0%
2.5 cm
mark
0%
1 cm
mark
0%
8 cm
mark
Explanation
|B|_{net}=0
(\dfrac{\mu _{0}i_{1}}{2\pi r_{1}})-(\dfrac{\mu _{0}i_{2}}{2\pi r_{2}})=0
where
r1
and
r_2
are distances from wires respectively.
Assuming the distance from wire 1 is
x
, then distance from wire 2 will be
2-x
\dfrac{i_{1}}{x}=\dfrac{i_2}{2-x}
\dfrac{1}{x}=\dfrac{3}{2-x}
4x=2
x=0.5 cm
from
1A
wire.
distance from the y-axis
2+0.5=2.5cm
.
Two infinitely long straight conductors which are held parallel to each other at a distance
0.4m
carry currents
20A
and
10A
in the same direction. The magnetic induction at a point midway between them is
Report Question
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10^{-5}T
0%
3\times 10^{-5}T
0%
2\times 10^{-5}T
0%
10^{-6}T
Explanation
\left | B \right |=(\dfrac{\mu _{0}i_{1}}{2\pi r_{1}})-(\dfrac{\mu _{0}i_{2}}{2\pi r_{2}})
=
(\dfrac{2\times 10^{-7}\times 20}{0.2})-(\dfrac{2\times 10^{-7}\times 10}{0.2})
=
50\times 2\times 10^{-7}T
=
10^{-5}T
An experimenters diary reads as follows : A charged particle is projected in a magnetic field
(7\hat{i}-3\hat{j}) \times10^{-3}
T . The acceleration of the particle is found to be
(\hat{i}+7\hat{j}) \times10^{-6}ms^{-2}
then coefficient of
\hat{i}
is
Report Question
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3.0
0%
7.0
0%
5.0
0%
4.0
Explanation
\bar{F}=q\left ( \underset{V}{\rightarrow}\times \underset{B}{\rightarrow} \right )
m\bar{a}=q(\bar{V}\times \bar{B})
\therefore \bar{a}.\bar{B}=0
(\hat{i}+7\hat{j}).(7\hat{i}-3\hat{j})=0
7x -21=0
x=3
When two infinitely long parallel wires separated by a distance of
1m
, each carry a current of
3A
, the force in newton/metre length experienced by each will be, (given
\mu _{0}=4\pi \times 10^{-7}
S.I. Units).
Report Question
0%
2\times 10^{-7}
0%
3\times 10^{-7}
0%
6\times 10^{-7}
0%
18\times 10^{-7}
Explanation
F = I LB
B=\dfrac{\mu_{o} I_{2}} {2\pi d}
L = 1 m
I = 3 A
I_{2} =3 A
d = 1 m
\implies F =
\dfrac{3\times 1\times 4\pi \times10^{-7} \times 3}{2\pi}
=
18\times 10^{-7}
N
Answer. D
The ratio of magnetic field at the centre of a current carrying coil to its magnetic moment is
x
. If the current and radius both are doubled, the new ratio will become:
Report Question
0%
2x
0%
4x
0%
x/4
0%
x/8
Explanation
Magnetic field at center of current carrying coil is,
B=\dfrac{\mu_oi}{2r}
Magnetic moment is given by:
M=i\pi r^2
Given ratio is:
x=\dfrac{B}{M}
x=\dfrac{\mu_o}{2\pi r^3}
On doubling the current and radius,
x'=\dfrac{\mu_0}{2\pi \times (2r)^3}
\therefore x'=\dfrac{x}{8}
0:0:1
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Practice Class 12 Medical Physics Quiz Questions and Answers
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