Two horizontal metal plates each 100 cm square are aligned...

Two horizontal metal plates, each 10.0 cm square, are aligned 1.00 cm apart with one above the other. They are given equal-magnitude charges of opposite sign so that a uniform downward electric field of $2.00 \times 10^{3} \mathrm{N} / \mathrm{C}$ exists in the region between them. A particle of mass $2.00 \times$ $10^{-16} \mathrm{kg}$ and with a positive charge of $1.00 \times 10^{-6} \mathrm{C}$ leaves the center of the bottom negative plate with an initial speed of $1.00 \times 10^{5} \mathrm{m} / \mathrm{s}$ at an angle of $37.0^{\circ}$ above the horizontal. (a) Describe the trajectory of the particle. (b) Which plate does it strike? (c) Where does it strike, relative to its starting point?

Transcript

00:01 Okay, so this is the graph of these questions.

00:03 So there's a positive particle lying in the middle of the negative plates, okay? and the electric field has a direction from positive plates to the negative plate, which is point downward.

00:17 So therefore, the trajectory of the particle should be a parabola, okay? because its initial speed was at an angle, which is about 37 degrees above the horizontal.

00:29 So it eventually fall down due to the electric field from this graph.

00:36 So eventually it will fall down on the bottom place, which is the negative place here.

00:43 And this explains question b.

00:47 And well, we know that since the particle was having an initial speed that was at an angle of 37 degree above the horizontal.

00:59 So that means the particle will move along the horizontal direction and the vertical direction simultaneously, which means that so if this is the speed of the velocity of the particle, let's say v, so we can decompose the velocity here with x component and y components, okay? and it will move along the y axis and x axis simultaneously, okay? so therefore, the time of the motion along the either direction should be the same.

01:36 Okay.

01:38 So now let's try to determine the acceleration that was acted on the particle first.

01:43 Okay? so while first we know the force, the net force, is equal to the electric force from this question, which is equal to charge times the electric field, which can be also equal to mass times acceleration, okay? therefore we can determine acceleration a is just simply equal to qe over m, okay? and charge q, which is the charge of particles, given as 1 .00 times 10 to the power of negative 6, coolant.

02:21 And the electric fuel is given as 2 .00 times 10 to the power of 3, new term of cologne.

02:29 And we know the mass, the wrong question was given as 2 .00 times 10 to the power of negative 16.

02:41 Therefore, the acceleration a should be equal to 1 times 10 to the power of 3, i'm sorry, not 3, 13 meter per second square, okay? and if we take look the free body diagram on the positive charged particle, so when it's in the air, it should look something like this.

03:10 So if this black die here is the is the positive charged particle, so you only experience a force that was pointing downward, which is the electric force, okay, which is equal to qe.

03:25 But remember, along the vertical directions, the particle is moving upward since it has an initial speed about 1 times 10 to the power 5 meter per second at an angle 37 degree above the horizontal.

03:40 So it should move like this along the y -axis.

03:44 Okay, so this is a speed of particle, which means that the acceleration on the particle is in the opposite direction when compared with the speed of a positive particle along the wide.

03:58 Direction.

03:58 Let's say here is vy since it's a vertical direction, okay? and this is acceleration a.

04:06 So therefore, vyi, which is the initial speed of the particle along the y -axis minus at should be equal to the final speed along the y -axis.

04:31 It's because the direction of the acceleration is opposite with the speed of a particle along the y -i direction.

04:39 Okay...

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