7. An electron enters a magnetic field in between two...

7. An electron enters a magnetic field in between two parallel charged plates with distance of 15 mm shown in diagram below. -150 V v 15 mm +150 V The velocity of the electron is 4.2 x 10^6 ms^-1. If the electron continues to move in a straight line without any deflection, what is the magnitude and direction of the magnetic field? A. 2.4 mT, out of the page B. 4.8 mT, out of the page C. 5.2 mT, into the page D. 7.3 mT, into the page

Transcript

00:01 In this problem, an electron enters a magnetic field in between two parallel charged plates with distance of 15 mm and the velocity of electron is given.

00:13 If the electron continues to move in a straight line without any deflection, we have to find out the magnitude and direction of the magnetic field.

00:26 So first we have to find out the electric field between the plates which is equal to potential difference divided by separation of plates.

00:34 Now the potential difference will be the potential of the positive plate minus the potential of the negative plate and separation of plates is 15 mm.

00:50 So the potential difference is 300 v and 15 mm is 15 times 10 -3 m.

00:59 So the electric field is 20 ,000 v per meter.

01:07 This is the electric field and it will be from the positive plate to the negative plate.

01:11 So the electric field will be in the upward direction and for this problem we will take the upward direction as positive y -axis, direction to the right as positive x -axis and direction out of page as positive z -axis.

01:30 Now the net force will be equal to sum of electric force and the magnetic force.

01:41 Now electric force is charge times electric field and magnetic force is charge times cross product of velocity and magnetic field.

01:56 So from this we get e plus v cross b equal to 0.

02:05 So v cross b is equal to minus e.

02:19 Now the velocity is along positive x -axis because it is to the right.

02:23 So it can be written as 4 .2 times 10 to the power 6 meter per second i where i is the unit vector along x -axis.

02:39 Cross product with magnetic field which is bxi byj plus bzk.

02:59 Bx, by and bz are the three components of the magnetic field equal to minus electric field.

03:07 Electric field is in the upward direction which means it is along the positive y -axis.

03:12 So it is 20000 volts per meter j.

03:17 Now on the left hand side we get 4 .2 times 10 to the power 6 meter per second times i cross bxi plus i cross byj plus i cross bzk equal to minus 20000 volts per meter j.

03:53 Now i cross i is 0...

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