Frequency of Revolution (a) Find the frequency of revolution of an electron with an energy of 10

Frequency of Revolution (a) Find the frequency of revolution...

Key Concepts

Kinetic Energy and Particle Velocity

This concept relates the kinetic energy of a particle to its speed, using the relation (1/2)mv² = energy. For particles given an energy value (like 100 eV), this equation allows one to calculate the velocity, which is essential when determining other motion parameters like the radius of the path in a magnetic field.

Lorentz Force

This concept refers to the force exerted on a charged particle moving in a magnetic field. The force, given by F = q(v × B), causes the particle to undergo circular motion when its velocity is perpendicular to the magnetic field. It provides the necessary centripetal force for the particle to maintain a curved path.

Cyclotron Frequency

Cyclotron frequency is the frequency at which a charged particle orbits in a uniform magnetic field. It is defined as f = qB/(2?m), where q is the charge of the particle, B is the magnetic field strength, and m is the particle’s mass. Notably, this frequency is independent of the particle’s speed, making it a key parameter in devices like cyclotrons.

Radius of Circular Motion

The radius of the circular path of a charged particle moving perpendicular to a magnetic field is given by r = mv/(qB). This formula arises by equating the magnetic (Lorentz) force to the centripetal force required for circular motion, linking the particle’s mass, velocity, charge, and the magnetic field strength.

Transcript

00:01 Over here we have information that 5th frequency of revolution of electron with the energy with with with an energy of 100 electron volt.

00:11 100 electron volt okay and what more so in the first part what more information we have is that is which is in the magnetic field of 95 micro tesla i guess so what will be the what will the frequency so frequency we know that frequency f will be nothing but bq upon 2 pi m e frequency f upon bq upon 2 bq b b b b q upon 2 pi m okay so this comes out to be b there is 35 into 10 to the bar minus 6 into q q of electron that only may include right so that is 1 .6 to 10 .19 upon 2 pi into mass of electron that is 1 .9 .1 into 10 to the bar of minus 31 i guess it comes out to be 9 .7 and you 10 to the bar of 19 5 .9 .78 into 10 to the power of 5 hearts okay and in the next part what we need to find is that how what is we calculate the radius of the path if of this electron if a velocity or perpendicular to the manate field so if velocity is perpendicular to the magnetic hill that means so what will do the radius so this radius will be nothing but you know r equal to mv upon qb right right so we have information of several things right so how we can find that mass we know but what we don't know we don't know velocity we know q we know b okay so first of all we need to find the velocity how well we can find so we know that frequency f equal to nothing but v upon 2 pi r i guess right v upon 2 pi r but there is one more we have to find the frequency how we can find the velocity and energy we have given 100 electron volt right if we have a hundred electron volt that means kinetic energy is given so half and v.

02:38 Square equal to 100 electron volt okay so half of mass of electron 9 .1 into 20 or minus 31 kg into v .s square equal to 100 and this is in the electron volt that is 1 .620 or minus 19 so this will be a hundred into 2.

02:53 So 200 is here we 10 to the power of minus 12 and so v square will be nothing but 200 into 1 .6 upon 10 to the power of 12 and upon 9 .1.

03:09 Okay so it comes out to be 10 to the power of 14 10 to the power of 14 into 3 .2 upon 9 .1.

03:22 So 3 .2 is divided by 9 .1.

03:25 So how about we do this? so 3 .2.

03:28 Divided by 9 .1.

03:30 So this comes up to be 0 .3516...

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