Two protons separated by a distance 'r' travelling n the same direction with velocity 'v' show that the ratio of magnetic and electric forces acting between them is (v/c)^2, c is the speed of light.
Asked by Tanya raj | 21st Aug, 2015, 08:19: PM
Expert Answer:
The electric force between the two protons is given as
Now, the magnetic force is given as FB = qvB
To find B:
The magnetic field is given from Biot-Savarts law as
dL is the length element of the conductor. However, we do not have any conductor here, but only protons moving.
So, the expression will be altered for charge and not current.
We know that I = q/t, so in time dt, the current moves a length dL. So, we get
I dL = q dL/dt = qv
Hence, the magnetic field is
Therefore, the magnetic force is given as
Hence, the ratio of electric and magnetic forces is
Now, we know that the speed of light is given as
Therefore, we get the ratio as
The electric force between the two protons is given as
Now, the magnetic force is given as FB = qvB
To find B:
The magnetic field is given from Biot-Savarts law as
dL is the length element of the conductor. However, we do not have any conductor here, but only protons moving.
So, the expression will be altered for charge and not current.
We know that I = q/t, so in time dt, the current moves a length dL. So, we get
I dL = q dL/dt = qv
Hence, the magnetic field is
Therefore, the magnetic force is given as
Hence, the ratio of electric and magnetic forces is
Now, we know that the speed of light is given as
Therefore, we get the ratio as
Answered by Romal Bhansali | 22nd Aug, 2015, 09:05: PM
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