two protons are moving in a given magnetic field with speed v and 3v perpendicular to the magnetic field. then the ratio of the magnetic force acting on them is
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12th
Physics
Moving Charges and Magnetism
Lorentz Force
Two protons move parallel t...
PHYSICS
Two protons move parallel to each other, keeping distance r between them, both moving with same velocity
v
. Then the ratio of the electric and magnetic force of interaction between them is:
(c - Velocity of light)
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ANSWER
There are two forces electric force and magnetic force experienced by proton.
The electric force between the two protons is given as
F
E
=
4πε
0
1
r
2
q
2
Now, the magnetic force is
F
B
=qvB
B is the magnetic field.
From Biot- savarts law
B=
4π
μ
0
r
2
IdL
dL is the length element of the conductor but, the expression will be for charge where is no current.
So,
we know that,
I=
t
q
IdL=q
dt
dL
IdL=qv
Now, the magnetic field is
B=
4π
μ
0
r
2
qv
The magnetic force is
F
B
=qvB
F
B
=qv
4π
μ
0
r
2
qv
F
B
=
4π
μ
0
r
2
q
2
v
2
Now, the ratio of the electric force and the magnetic force is
F
B
F
E
=
4π
μ
0
×
r
2
q
2
v
2
4πε
0
1
×
r
2
q
2
F
B
F
E
=
μ
0
ε
0
v
2
1
......(I)
We know that, the speed of light
c=
μ
0
ε
0
1
c
2
=
μ
0
ε
0
1
Now, put the value of
μ
0
ε
0
1
in equation (I)
F
B
F
E
=
v
2
c
2
Hence, the ratio of electric force and magnetic force will be
F
B
F
E
=
v
2
c
2
.