00:01
Hello, the question is taken from electricity and magnetism and the question is an electron follows an helical path in uniform magnetic field of magnitude 0 .3 tesla.
00:14
The pitch of the path is 6 meter and the magnitude 6mm and the magnitude of the magnetic force on the electron is 2 .10 to the power minus 15 newton.
00:28
What is the electron speed? so given that b is equal to 0 .3 tesla and the pitch is equal to so that distance is already given to us and having value is equal to 6 meter okay so and the magnitude of magnetic force f is equal to 2 into 10 to the power minus 15 newton so what will be the value of electron speed so we know that pitch is basically when electron travels this helical path that distance is a cold pitch so pitch is basically the distance travelled in one time period so we can write and that corresponding to the horizontal velocity so v parallel is equal to parallel component of the velocity is equal to distance over time period distance is x divided by time period so that will be equal to six over time period okay now we know that vertical force vertical velocity basically in the presence of magnetic field corresponding to the circular motion so that circular motion is basically contributed by the vertical component velocity and that is that force will be equal to centripetal force mv perpendicular square by r okay so we perpendicular will be cancelled out and so that will be perpendicular is equal to q b r over m we know that t is equal to 2 pi r over v perpendicular so we perpendicular so here we also need the time period value so we parallel will be equal let us substitute the value of v perpendicular here we get time period is equal to 2 pi r divided by qb r and m here.
02:39
R will be cancelled out.
02:40
So t will be equal to 2 pi m over qb.
02:44
Q is basically the charge on electron, so that will be eb.
02:47
Substituting this, let us first evaluate the time period.
02:51
So time period will be equal to 2 into 3 .14.
02:55
Mass on electron is equal to 9 .1 into 10 to the power minus 31.
03:00
Charge on electron is equal to 1 .6 into 10 to the power minus 19.
03:04
And b is equal to 0 .3 so that will give us the value of time period of electron is equal to 2 into 3 .14 into 9 .1e minus 31 divided by 1 .6e minus 19 further divided by 0 .3 so that will gives us 1 .2 into 10 to the power minus 10 seconds which is the required value of time period now let us evaluate the value of v parallel v parallel is equal to 6 over t so that will be 6 over 1 .2 into 10 to the power minus 10 so that will be equal to 60 divided by 12 into 10 to the power 10 so that will be 5 v parallel i think something wrong with it minus 31 plus 19 so that is minus 12 any other thing that we need to substitute the value of force and the case of electron i think something wrong with the statement i think the value of pitch is in micrometer so that will be i think micrometer i by mistakenly written as meter so that distance is micrometer so that will be 10 to the power minus 6 so substituting here the value of 16 to 10 to the power minus 6.
04:57
Multiply 10 to the power minus 6.
04:59
So if we solve it, that value become 10 to the power minus 6 plus 10 to the power 10 is 10 to the power 4.
05:08
So that will be 5 into 10 to the power 4 meter per second.
05:12
Now let us evaluate the value of v perpendicular...