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# A proton projected in a magnetic field of 0.020 T travels along a helical path of radius 5.0 cm and pitch 20 cm. Find the components of the velocity of the proton along and perpendicular to the magnetic field. Take the mass of the proton = 1.6 × 10^{–27} kg.

Answer :

Given

Mass of the proton, *m _{p}* = 1.6 × 10

^{−27}kg

Magnetic field intensity, *B* = 0.02 T

Radius of the helical path, *r* = 5 cm = 5 × 10^{−2} m

Pitch of the helical path, *p* = 20cm = 2 × 10^{−1} m

In helical motion we have two components of velocity.

Component of velocity which is perpendicular to the magnetic field is given by -

Similarly component of velocity in the direction of magnetic field will be the parallel component given by -

Now,

Now, this force is balanced by Lorentz force acting due to presence of magnetic field ,

⇒

Now, pitch of the helix is calculated as –

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