An electron (mass = 9.11 x 10^-31 kg) traveling with a...

An electron (mass = 9.11 x 10^{-31} kg) traveling with a horizontal speed v = 2.00 x 10^6 m/s, enters a uniform electric field of 5.50 x 10^6 N/C created by two charged parallel plates. The electron enters exactly midway between the plates, and is deflected upwards as it travels, eventually hitting the upper plate. a) What is the direction of the electric field between the parallel plates? [1] b) What is the magnitude of the acceleration of the electron? [1] c) How long does it take for the electron to hit the upper plate, from the time it enters the electric field? [1] d) What horizontal distance, d, does the electron travel before hitting the upper plate? [1] d v h = 3.00 cm

Transcript

00:01 So this question is asking us about some kinematics of an electron moving between the plates of a capacitor.

00:13 We are told that the electric field between the plates of the capacitor is 5 .5 times 10 to the 6 newtons per kulum.

00:29 And we're told that the electron is deflected upwards as it travels.

00:36 Now, the electron is a negative charge, and the direction of the electric field goes in the direction that a positive charge would experience a net force.

00:46 So if the electron is deflected upwards, a positive charge be deflected downwards.

00:51 So the answer to the first question is the direction of the electric field must be downwards.

01:02 Now, the second question is, what is the magnitude of the acceleration? well, we can find the force on the electron using this uniform electric field and multiplying the electric field times the charge gives us the electric force.

01:18 So the electric force would be equal to q times e.

01:23 So using newton's second law, the acceleration would be the force divided by the mass of electron.

01:35 So that's going to equal q times e over the mass electron.

01:41 And that gives us 1 .6 times 10 to the minus 19 coulons times times 5 .5 times 10 to the 6 newtons per coulomb.

02:02 Divided by the mass, that is this is force, divided by the mass, which is 9 .11 times 10 to the minus 31 kilograms.

02:14 And when you calculate all that out, what you get in your calculator is 9 .67 times 10 to the 17 meters per second square.

02:33 I've kept more digits that i should be allowed to by the number of significant digits we have.

02:37 Looks like we have three...

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