Assume the region to the right of a certain vertical plane...

Assume the region to the right of a certain vertical plane contains a vertical magnetic field of magnitude 2.00\times 10^{-4}T and the field is zero in the region to the left of the plane. An electron, originally traveling perpendicular to the boundary plane, passes into the region of the field. Assuming the maximum depth of penetration into the field is 4.25cm. Noting that its path is a semicircle. What is the bending direction when the electron enter the magnetic field region? upward downward out of the page into the page moving straight

Transcript

00:01 Hello everyone in this problem it is given to the right of a certain vertical plane there is a uniform magnetic field so suppose this is the plane so here is the magnetic field that is uniform but to the left there is no magnetic field from the boundary of the electric field sorry from the boundary of uniform magnetic field of 1 .0 into 10 to the power minus 3 tesla electron is projected then for how long it will be in the magnetic field that we have to find the time taken to come out from the magnetic field that we have to calculate and in second part we have to find that kinetic energy of electron if depth of penetration this depth of penetration in the magnetic field is 2 .0 centimeter that is 2 into 10 to the power of minus 2 meter because it is completing the half cycle so this will be the radius now we start solving in the first part we have to calculate how long it will move through the magnetic field since it is completing the half cycle in the magnetic field so we it would be half of time period of revolution and time period of revolution of a charged particle in the magnetic field is 2 pi m upon bq.

01:44 So it would be pi m upon bq.

01:49 Now substitute the value.

01:51 P is 3 .14.

01:54 Mass of electron you know 9 .1 into 10 to the power of minus 31 k .magnetic fill is 1mill is 1mille tesla, that is 1 into 10 to the power minus 3 tesla and charge on electron is 1 .6 into 10 to the power of minus 19 kulem.

02:15 So, so.

02:16 So the time for it is moving in the magnetic field is 1 .79 into 10 to the power of minus 8 seconds.

02:26 So this is the answer of first part.

02:32 In second part we have to calculate kinetic energy.

02:36 To calculate the kinetic energy, first we required the velocity.

02:40 As you know that, radius of the circular path described by the charge in the magnetic field is mv upon bq.

02:46 So from here, velocity would be bqr y m.

02:53 Hence, kinetic energy will be half m b square...

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