When charge particle enter perpendicular to magnetic field, the path followed by it is
a)A helix
b)A circle
c)Straight line
d)Ellipse
And plz explain
Answers
Answered by
1
When a charged particle enters a magnetic field, it experience Lorentz force given by: dpdt=qv⃗ c×B⃗ dpdt=qv→c×B→
Since the force is cross product of particle’s velocity and magnetic field, it will be perpendicular to the direction of motion — the force does no work on the charge particle. Thus, the kinetic energy is unchanged—speed of the particle remains the same. The only thing it can change is the direction of the motion.
You can find the radius and time period of the circular motion by equating the above expression of mechanical force with the centripetal force give by: Fc=mv2r.
Since the force is cross product of particle’s velocity and magnetic field, it will be perpendicular to the direction of motion — the force does no work on the charge particle. Thus, the kinetic energy is unchanged—speed of the particle remains the same. The only thing it can change is the direction of the motion.
You can find the radius and time period of the circular motion by equating the above expression of mechanical force with the centripetal force give by: Fc=mv2r.
Answered by
7
hi mate
When a charged particle enters a magnetic field, the field exerts a force on the charged particle given by F⃗ =q(v⃗ ×B⃗ ), where F,q,vand Bare the force, charge on the particle, velocity of the particle and the magnetic field strength respectively.
The direction of v⃗ ×B⃗ is the direction of the force exerted on a positively charged particle.
In case of a negatively charged particle, the force is in the opposite direction.
⇒|F⃗ |=|q|v⃗ |×|B⃗ |sinθ,where θ is the angle between v⃗ and B⃗ .
If θ=0°or 180°,there is no force acting on the particle and the particle continues to move with uniform velocity.
If θ=90°, the force acting on the particle is the maximum possible and the direction of the force is perpendicular to the path of the particle. The particle then moves along a circular path with the force acting as the centripetal force.
When θ has some other value, we can resolve the velocity into the direction perpendicular to B⃗ and the direction parallel to B⃗ .
The component of the velocity in the direction parallel to B⃗ will not be affected by the magnetic field. However, the component of the velocity in the direction perpendicular to B⃗ will subjected to a force of the magnetic field which would result in a uniform circular motion.
Hence the particle would have a component motion along a straight line as well as a circular component. Therefore the path of the charged particle would be in the form of a helix.
When a charged particle enters a magnetic field, the field exerts a force on the charged particle given by F⃗ =q(v⃗ ×B⃗ ), where F,q,vand Bare the force, charge on the particle, velocity of the particle and the magnetic field strength respectively.
The direction of v⃗ ×B⃗ is the direction of the force exerted on a positively charged particle.
In case of a negatively charged particle, the force is in the opposite direction.
⇒|F⃗ |=|q|v⃗ |×|B⃗ |sinθ,where θ is the angle between v⃗ and B⃗ .
If θ=0°or 180°,there is no force acting on the particle and the particle continues to move with uniform velocity.
If θ=90°, the force acting on the particle is the maximum possible and the direction of the force is perpendicular to the path of the particle. The particle then moves along a circular path with the force acting as the centripetal force.
When θ has some other value, we can resolve the velocity into the direction perpendicular to B⃗ and the direction parallel to B⃗ .
The component of the velocity in the direction parallel to B⃗ will not be affected by the magnetic field. However, the component of the velocity in the direction perpendicular to B⃗ will subjected to a force of the magnetic field which would result in a uniform circular motion.
Hence the particle would have a component motion along a straight line as well as a circular component. Therefore the path of the charged particle would be in the form of a helix.
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